I think if you were to separate the code into different files you might have a better time moving around.
What I recommend is that you pass the characteristic and device ID to the fragment using a bundle:
    public static MyFragment newInstance(int someInt) {
        MyFragment myFragment = new MyFragment();
        Bundle args = new Bundle();
        args.putString("someInt", someString);
        myFragment.setArguments(args);
        return myFragment;
    }
    //-------
    // In the fragment
    getArguments().getInt("someString");
I have been writing some pretty abismal code for a few years but it does get a lot of the heavy lifting out the way:
    //By the way, I think this is the server, better known as "Central Module", not the peripheral. I've had this misunderstanding until recently and still need to change the code
    public class BLEPeripheral {
        private String deviceId;
        private BLEManager connector;
        private BluetoothAdapter bluetoothAdapter;
        private BluetoothLeScanner bluetoothLeScanner;
        private BluetoothGatt bluetoothGatt;
        private BluetoothGattService bluetoothGattService = null;
        private HashMap<String, Command<String>> subscriptions;
        private boolean connected = false;
        public boolean isConnected() {
            return connected;
        }
        public BLEPeripheral(BLEManager connector, String deviceId) {
            this.connector = connector;
            this.deviceId = deviceId;
            this.connector.onDisconnected();
            final BluetoothManager bluetoothManager = (BluetoothManager) this.connector.getContext().getSystemService(Context.BLUETOOTH_SERVICE);
            bluetoothAdapter = bluetoothManager.getAdapter();
            if (bluetoothAdapter == null || !bluetoothAdapter.isEnabled()) {
                this.connector.enableBluetooth();
                return;
            }
            if (!this.connector.checkPermission()) return;
            scanForDevice();
        }
        public void scanForDevice() {
            connected = false;
            connector.log("BT ENABLED: SCANNING FOR DEVICES");
            connector.reportState(BleManagerStatus.SEARCH_START);
            bluetoothLeScanner = bluetoothAdapter.getBluetoothLeScanner();
            bluetoothLeScanner.startScan(mLEScanCallback);
        }
        public void stopScan() {
            connector.reportState(BleManagerStatus.SCAN_CANCEL);
            bluetoothLeScanner.stopScan(mLEScanCallback);
        }
        private final ScanCallback mLEScanCallback = new ScanCallback() {
            @Override
            public void onScanResult(int callbackType, ScanResult result) {
                BluetoothDevice device = result.getDevice();
                ScanRecord record = result.getScanRecord();
                if (record == null) {
                    connector.log(String.format("Device [%s] has no scan record", device.getAddress()));
                    return;
                }
                String name = record.getDeviceName();
                String UUID = null;
                if (record.getServiceUuids() != null) {
                    for (ParcelUuid pId : record.getServiceUuids()) {
                        if (pId.getUuid().toString().equals(deviceId)) {
                            UUID = pId.getUuid().toString();
                        }
                    }
                }
                if (UUID == null) {
                    if (name != null) connector.log(String.format("Discovered Device [%s]. Continuing search", name));
                    return;
                }
                connector.log(String.format("Peripheral [%s] located on Device [%s]. Attempting connection", UUID, name));
                bluetoothGatt = device.connectGatt(connector.getContext(), true, mGattCallback);
                stopScan();
                connector.reportState(BleManagerStatus.DEVICE_FOUND);
                super.onScanResult(callbackType, result);
            }
        };
        private void closeGatt() {
            connector.reportState(BleManagerStatus.DICSONNECT);
            connector.onDisconnected();
            if (bluetoothGatt == null) {
                return;
            }
            bluetoothGatt.close();
            bluetoothGatt = null;
            scanForDevice();
        }
        private final BluetoothGattCallback mGattCallback = new BluetoothGattCallback() {
            StringBuilder buffer;
                    @Override
                    public void onConnectionStateChange(BluetoothGatt gatt, int status, int newState) {
                        connector.onConnectionStateChange(newState);
                        if (newState == BluetoothProfile.STATE_CONNECTED) {
                            connector.log("Connected to device GATT. Discovering services");
                            connector.reportState(BleManagerStatus.DEVICE_CONNECTED);
                            bluetoothGatt.discoverServices();
                        } else if (newState == BluetoothProfile.STATE_DISCONNECTED) {
                            connector.log("Disconnected from GATT server. Continuing scanning");
                            closeGatt();
                        }
                    }
                    @Override
                    public void onServicesDiscovered(BluetoothGatt gatt, int status) {
                        if (status == BluetoothGatt.GATT_SUCCESS) {
                            if (bluetoothGatt.getServices() != null) {
                                connector.log("Services discovered: ["+bluetoothGatt.getServices().size()+"]");
                                for (BluetoothGattService service : bluetoothGatt.getServices()) {
                                    if (service.getUuid().toString().equals(deviceId)) {
                                        bluetoothGattService = service;
                                        connector.onConnected();
                                        connector.log("Service discovered");
                                        connector.log("Attempting characteristic subscription");
                                        connector.subscribeToCharacteristics();
                                    }
                                }
                            }
                        } else {
                            connector.log(String.format("onServicesDiscovered received: [%s]", status));
                        }
                    }
                    @Override
                    public void onCharacteristicRead(BluetoothGatt gatt, BluetoothGattCharacteristic characteristic, int status) {
                        if (status == BluetoothGatt.GATT_SUCCESS) {
                            connector.log(String.format("onCharacteristicRead received: [%s] value: [%s]", characteristic.getUuid().toString(), new String(characteristic.getValue())));
                        } else {
                            connector.log(String.format("onCharacteristicRead fail received: [%s]", status));
                        }
                    }
                    @Override
                    public void onCharacteristicWrite(BluetoothGatt gatt, BluetoothGattCharacteristic characteristic, int status) {
                        super.onCharacteristicWrite(gatt, characteristic, status);
                        if (status == BluetoothGatt.GATT_SUCCESS) {
                            connector.log(String.format("onCharacteristicWrite received: [%s] value: [%s]", characteristic.getUuid().toString(), new String(characteristic.getValue())));
                        }
                    }
                    @Override
                    public void onCharacteristicChanged(BluetoothGatt gatt, BluetoothGattCharacteristic characteristic) {
                        String packet = new String(characteristic.getValue());
                        if (packet.equals(String.valueOf((char)2))) {
                            buffer = new StringBuilder();
                        } else if (packet.equals(String.valueOf((char)3))) {
                            if (subscriptions == null || subscriptions.size() == 0) return;
                            Command<String> handler = subscriptions.get(characteristic.getUuid().toString());
                            if (handler != null) handler.execute(new String(buffer.toString()));
                        } else {
                            buffer.append(packet);
                        }
                    }
                };
        public BluetoothGattService getService() {
            return bluetoothGattService;
        }
        private BluetoothGattCharacteristic findCharacteristicById(String id) {
            if (bluetoothGattService.getCharacteristics() != null) {
                return bluetoothGattService.getCharacteristic(java.util.UUID.fromString(id));
            }
            return null;
        }
        public void subscribe(String characteristicId, Command<String> handler){
            if (subscriptions == null) subscriptions = new HashMap<>();
            BluetoothGattCharacteristic characteristic = findCharacteristicById(characteristicId);
            if (characteristic == null) {
                connector.log("Characteristic does not exist");
                return;
            }
            connected = true;
            connector.reportState(BleManagerStatus.CHARACTERISTIC_SUBSCRIBED);
            bluetoothGatt.setCharacteristicNotification(characteristic, true);
            BluetoothGattDescriptor descriptor = characteristic.getDescriptor(UUID.fromString("00002902-0000-1000-8000-00805f9b34fb"));
            descriptor.setValue(BluetoothGattDescriptor.ENABLE_NOTIFICATION_VALUE);
            bluetoothGatt.writeDescriptor(descriptor);
            subscriptions.put(characteristicId, handler);
        }
        public void writeCharacteristic(String characteristicId, String data) {
            BluetoothGattCharacteristic characteristic = findCharacteristicById(characteristicId);
            if (characteristic != null) {
                characteristic.setValue(data);
                bluetoothGatt.writeCharacteristic(characteristic);
                connector.log(String.format("Wrote [%s] to [%s]", data, characteristicId));
            } else {
                connector.log(String.format("[%s] not found on device", characteristicId));
            }
        }
        public void readCharacteristic(String characteristicId) {
            BluetoothGattCharacteristic characteristic = findCharacteristicById(characteristicId);
            if (characteristic == null) return;
            bluetoothGatt.readCharacteristic(characteristic);
        }
    }
[SOURCE CODE]
Then I just need to pass an instance of BLEManager in, which is just a simple interface:
    public interface BLEManager {
        void log(String message);
        void reportState(BleManagerStatus status);
        void onConnectionStateChange(int newState);
        Context getContext();
        void enableBluetooth();
        void onConnected();
        void subscribeToCharacteristics();
        void onDisconnected();
        boolean checkPermission();
    }
[SOURCE CODE]
And your fragment / activity can just implement that. I think this is called an adapter pattern, because I'm abstracting the implementation of BLE away from the Android lifecycle.
- this a video of one of the things I did with it. I built the tank as well :)
- here is the Raspberry Pi part