I have become fond of the Mikuni flat slide carbs. They are very nice, and they are not very expensive. The round slide ones are even less expensive.
I would say that a 30mm or 32mm Mikuni would be fine. In fact, a 32mm Mikuni Flat Slide carb is what we normally recommend for all Bullets, but we are taking into account that they will stick with the one carb as they upgrade their power levels. IF you have no power upgrade plans which include increased breathing of the cylinder head, then a 30mm would do fine.
You'll need to re-jet any of these carbs, because they come jetted for other bikes which are not like ours.
30 pilot, p6 needle jet, 190 main would probably be a good jetting start for a stock bike and a Mikuni TM32-1.
Pilot jets are 22/210 type
Needle jets are 389 type
Main jets are 4/042 type.