As a rule, private hires are MUCH more expensive than the taxis and busses in Uganda. For example, a trip costing 1,500 ush via taxi is almost 30,000 ush via private hire. The busses are fine and a fraction of the cost. The bus park can be a bit overwhelming, especially if you aren't sure of which line you will be taking. Ask around in Kampala for the best bus line to bunyonyi. If a last resort, the bus lines employ touts at the bus park who will happily direct you to the right bus for a small tip (don't pay more than 5,000 ush or so). Most busses leave every hour, depending on when they fill up, and follow a relatively reliable time table. The busses are a bit bumpy and cramped, but it is definitely worth the savings. We recently took the bus from kampala to mbale with 18 very large boxes of children's books in tow and it was 10,000 ush pp, plus an additional 35000 for the cargo. This compared to the offer of 250,000 ush for the same trip from the private hire truck driver who brought us to the park.
If you still decide on a private driver, we highly recommend Dominic Kizito, who is a driver that our friends and ourselves have used in the past. He runs his own private tour company, and does private driving all over Uganda and Kenya. His contact info is www.assuredugandasafari.com, or Dominic@assuredugandasafari.com
Hope all this is helpful