I have to STRONGLY recommend driving. This is coming from someone who lives in New York and prefers to take the subway AND bus to driving in traffic, so it's not like I'm averse to public transportation. However, I have found Disney transportation to be: a) slow b) crowded c) unreliable and d) all of the above! There have been situations where we have waited 45 minutes for a Disney bus. In certain resorts, you have to wait for the bus to go all... the... way... around the entire resort (i.e. Caribbean Beach). And forget it if you're there after the park closes. The lines will make you wish you had a Fast Pass!
While some might consider it inconvenient that you generally have to wait for a tram to take you from the parking lot to the gate, there is another one along every minute. (And if you get there early enough, you might be able to walk it! Particularly at Epcot!)
As a PP mentioned the MK is the hardest to get to, because you have to take the monorail from the TTC. That might be the one to take the bus. However, if you're planning on staying until the park closes, it's easier to take the monorail to TTC than wait on a long line for a bus!
Getting from park to park is not easy on Disney Transportation either (your parking fee is good for the whole day so don't let that stop you) and forget it if you need to go hotel to hotel. You could (and we have) literally spend 2 hours trying to get from one hotel to another. For example, you spend the day at AK, then go to dinner at Jiko at AKL. You'll need to take a bus from AK to a park, and then switch to your hotel. I'm breaking out in hives just thinking about it!
At least you'll already have your car, so it's not like you have to make the decision to rent one. GL!