It will certianly fit and you should be fine. We have 3 little ones under the age of 5 and there is NO WAY that we could do WDW without our own stroller. I think we need it more for getting to and from the parks then we actually use it in the parks, so renting one has never been an option for us.
A few hints to make it a bit easier for traveling on the Disney buses and to keep your fellow vacationers a bit happier ...
1. DO NOT WAIT to fold your stroller at the door of the bus. I think this is one of the things that frustrates Non-stroller guests so much. I have a stroller and it really makes steam come out of my ears!
Since you know that you are going to have to fold it anyway, do so before the bus arrives. If your little one is asleep and you don't know how long it will be until the bus arrives, by all means, let him sleep. HOWEVER, do not keep other guests from getting on the bus while you empty your stroller, try and juggle everything and then fold it, just move to the side and let others past you.
I have found that when I do this I always have more then one person offering me their seat once we finally get on the bus. Most times there are people asking if they can help me get or the kids in any way.
2. Carry an empty bag in your stroller to put all the little things that you carry in your stroller in to when you fold it. Does that make sense? Fill the bag while waiting for the bus. That way, you only have the child, the stroller and one bag to carry on and off the bus.
I am always amazed at all the stuff that accumulates in the stroller basket!
3. Don't try and force yourself and your stroller on to an already overcrowded bus, just wait for the next one and be the first in line ... especially when leaving a park. The buses seem to come a bit faster at the end of the day so you shouldn't have too long of a wait.
Hope this helps! -Jennie