There's a library for handling public-private key pairs in Swift that I recently created called Heimdall, which allows you to easily export the X.509 formatted Base64 string of the public key.
To comply with SO rules, I will also include the implementation in this answer (so that it is self-explanatory)
public func X509PublicKey() -> NSString? {
    // Fetch the key, so that key = NSData of the public key
    let result = NSMutableData()
    let encodingLength: Int = {
        if key.length + 1 < 128 {
            return 1
        } else {
            return ((key.length + 1) / 256) + 2
        }
    }()
    let OID: [CUnsignedChar] = [0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86,
        0xf7, 0x0d, 0x01, 0x01, 0x01, 0x05, 0x00]
    var builder: [CUnsignedChar] = []
    // ASN.1 SEQUENCE
    builder.append(0x30)
    // Overall size, made of OID + bitstring encoding + actual key
    let size = OID.count + 2 + encodingLength + key.length
    let encodedSize = encodeLength(size)
    builder.extend(encodedSize)
    result.appendBytes(builder, length: builder.count)
    result.appendBytes(OID, length: OID.count)
    builder.removeAll(keepCapacity: false)
    builder.append(0x03)
    builder.extend(encodeLength(key.length + 1))
    builder.append(0x00)
    result.appendBytes(builder, length: builder.count)
    // Actual key bytes
    result.appendData(key)
    // Convert to Base64 and make safe for URLs
    var string = result.base64EncodedStringWithOptions(.allZeros)
    string = string.stringByReplacingOccurrencesOfString("/", withString: "_")
    string = string.stringByReplacingOccurrencesOfString("+", withString: "-")
    return string
}
public func encodeLength(length: Int) -> [CUnsignedChar] {
    if length < 128 {
        return [CUnsignedChar(length)];
    }
    var i = (length / 256) + 1
    var len = length
    var result: [CUnsignedChar] = [CUnsignedChar(i + 0x80)]
    for (var j = 0; j < i; j++) {
        result.insert(CUnsignedChar(len & 0xFF), atIndex: 1)
        len = len >> 8
    }
    return result
}
I have removed the data fetching code, refer to either source of Heimdall or Jeff Hay's answer