I use a boga myself.
Once I have the fish clipped, I secure the rod and go from there.
Most of the time I just clip it on, remove the fly and wave good bye (always with bluefish). If I'm looking to have a picture taken I hold the boga with my left, and side my right hand under the belly. The fish will thrash and this will often propel her right into your lap. If not I control with the boga and lift with my right arm.
Just have to be careful fishing around rips and the surfline - in those areas its best to just let it go quickly.