Yup , I have the same problem: Time
I'm just back from Uganda where, due to an enormous cluck up, I didn't get to ride more then 100yds but I can thoroughly recommend it as a place to visit (Good regular BA direct flights to Kampala).
I would probably warn agains hiring a 125cc. They won't be quick enough to keep up with traffic out of town so you could find yourself in the gutter being overtaken by lorries. OK for a day or two but wearing after 3 weeks I'd have thought (In fact that's why I didn't ride - I ordered a 250 but a very shonky 125 turned up)
I'm contemplating a trip from Mombasa, dropping down into Tanzania, looping up to Rwanda and back to Uganda. Should take 2-3 weeks and gives you a variety of countries
If you look on the 'Biking in Uganda' thread, there's mention of a very helpful chap I met in Kampala. I don't want to fall foul of advertising rules on here but give him a call if you are thinking about hiring in Uganda
Do it and you'll have a great time