Danny Ferry is no dummy. If he trades that Brooklyn pick it will be for a rotation player on a rookie contract. The absolute best you could hope for with Bass is the pick they just got from Minny, which is pretty protected. Even that would be unlikely.
But since I'm an amateur capologist, either of the following two deals would work for Bass:
Bass for Elton Brand + draft compensation (although Brand has veto rights, and may very well be willing to exercise them).
Bass for Jenkins and Muscala + draft compensation.
Both of those trades send back expiring/non-guaranteed contracts due to players at the end of the bench, and so make sense from a roster management perspective for both teams. It is very hard to fit Prince into the Hawks space -- those trades above each work with no more than about $200k room for the Hawks, and Prince makes $800k more than Bass.
Ad an aside, Woj speculated on Twitter that the space created by the Payne trade would be used on either Ray Allen or Gary Neal. I find that a bit of jumping to conclusions. The Hawks still have their room exception to offer to a free agent, and as John Jenkins is a 3-point specialist who doesn't get to play and is an expiring deal, he would be a natural candidate to be waived in order to make room for a 3-point specialist who would get to play. Payne was moved to create more cap room to acquire a bigger piece. Whether that bigger piece is successfully acquired is another matter, but he wasn't moved to make room for Ray Allen.