I can comment on the Uganda part to say that driving around in the west is tough as the roads are so bad. But of course if you drive slow you can see more animals along the road. I was recently out west, but in Queen Elizabeth park and saw lions, elephants, hippos, loads of primates and plenty of lion food (antelope and buffalo). I drove myself as I don't like tour guides and we had no problems.
But I can tell you it would be a long drive from Bwindi to Entebbe. And Entebbe to Jinja will take a good while. If you are thinking of spending more than 2-3 hours rafting you should spend the night in Jinja and start early. Then you could drive back to Entebbe in the afternoon. In general it's not a great idea to drive at night, even if you have a driver. I do it from time to time, but stuff happens at night.