You could leverage an XMLStreamWriter and an XmlAdapter to do this:
BobAdapter
Things to note about the XmlAdapter:
- It's stateful and references an XMLStreamWriter.  We will later leverage JAXB's ability to set a statefulXmlAdapteron aMarshaller.
- It converts from a List<String>to aList<String>, we're just using anXmlAdapterhere to get an event.
- The marshalmethod is where we callwriteProcessingInstructionon theXMLStreamWriter:
 
package forum6931520;
import java.util.List;
import javax.xml.bind.annotation.adapters.XmlAdapter;
import javax.xml.stream.XMLStreamWriter;
public class BobAdapter extends XmlAdapter<List<String>, List<String>> {
    private boolean first = true;
    private XMLStreamWriter xmlStreamWriter;
    public BobAdapter() {
    }
    public BobAdapter(XMLStreamWriter xmlStreamWriter) {
        this();
        this.xmlStreamWriter = xmlStreamWriter;
    }
    @Override
    public List<String> marshal(List<String> stringList) throws Exception {
        if(first) {
            xmlStreamWriter.writeProcessingInstruction("array", "bob");
            first = false;
        }
        return stringList;
    }
    @Override
    public List<String> unmarshal(List<String> stringList) throws Exception {
        return stringList;
    }
}
Alice
The @XmlJavaTypeAdapter annotation is used to link the XmlAdapter with the field/property:
package forum6931520;
import java.util.List;
import javax.xml.bind.annotation.XmlRootElement;
import javax.xml.bind.annotation.adapters.XmlJavaTypeAdapter;
@XmlRootElement
public class Alice {
    private List<String> bob;
    @XmlJavaTypeAdapter(BobAdapter.class)
    public List<String> getBob() {
        return bob;
    }
    public void setBob(List<String> bob) {
        this.bob = bob;
    }
}
Demo
package forum6931520;
import java.io.File;
import javax.xml.bind.JAXBContext;
import javax.xml.bind.Marshaller;
import javax.xml.bind.Unmarshaller;
import javax.xml.stream.XMLOutputFactory;
import javax.xml.stream.XMLStreamWriter;
public class Demo {
    public static void main(String[] args) throws Exception {
        JAXBContext jc = JAXBContext.newInstance(Alice.class);
        File xml = new File("src/forum6931520/input.xml");
        Unmarshaller unmarshaller = jc.createUnmarshaller();
        Alice alice = (Alice) unmarshaller.unmarshal(xml);
        Marshaller marshaller = jc.createMarshaller();
        XMLOutputFactory xof = XMLOutputFactory.newFactory();
        XMLStreamWriter xmlStreamWriter = xof.createXMLStreamWriter(System.out);
        marshaller.setAdapter(new BobAdapter(xmlStreamWriter));
        marshaller.marshal(alice, xmlStreamWriter);
    }
}
input.xml
<?xml version="1.0" encoding="UTF-8"?>
<alice>
  <?array bob?>
  <bob>edgar</bob>
  <bob>david</bob>
</alice>
Output
<?xml version='1.0' encoding='UTF-8'?><alice><?array bob?><bob>edgar</bob><bob>david</bob></alice>
Note
This example needs to be run with EclipseLink JAXB (MOXy) as the JAXB RI will throw the following exception (I'm the MOXy lead):
Exception in thread "main" com.sun.xml.internal.bind.v2.runtime.IllegalAnnotationsException: 2 counts of IllegalAnnotationExceptions
java.util.List is an interface, and JAXB can't handle interfaces.
    this problem is related to the following location:
        at java.util.List
        at public java.util.List forum6931520.Alice.getBob()
        at forum6931520.Alice
java.util.List does not have a no-arg default constructor.
    this problem is related to the following location:
        at java.util.List
        at public java.util.List forum6931520.Alice.getBob()
        at forum6931520.Alice
For More Information
UPDATE
I have entered an enhancement request (https://bugs.eclipse.org/354286) to add native support for processing instructions.  This would eventually allow you to specify the following on your property:
@XmlProcessingInstruction(target="array", value="bob")
public List<String> getBob() {
    return bob;
}