Boda bodas got their name from the bicycle taxis that operated at some of the busy border crossing points. Buses had to discharge their passengers at the exit border control, who then had to walk to the entry border control. The distance across no man’s land at some borders can be considerable. Hence the bicycle taxis would cry “boda boda” (“border to border”) to the weary travellers. These bicycle taxis can still be found in most smaller Ugandan towns, however, in Kampala they have been replaced by scooters.
Source: WikiTravel.org: Kampala