I went last year for the first time, and also didn't have a car, but we did it the other way round, from universal end of international drive to disney. We will also be going back this year, (staying onsite), without a car again.
We found no problems getting buses, although we did have to get about 3 each way, and it was a bit tiring at the end of a long stay. You could look at the lynx bus website
www.golynx.com although we didn't find it helpful before the first time as we didn't know the names of all the places. We asked our rep, who gave us all the information, and the bus timetables.
A lot of people on the boards much prefer to take a car but as i am under 21, it was not an option for us because of the insurance. A lot of people also prefer to use companies like Mears or take town cars or taxis. As there was only two of us, it was much cheaper to take buses, however, this time there will be six of us so it will probably be easier for us to split the fare of a taxi or towncar and the little bit extra it will cost each will be worth it for the convenience.
All in all, once you find out which buses you need to get it's easy enough, but it can take a long time, and be tiring after a long day but it is doable!