We always rent a double stroller at the parks, you can pre-purchase the rentals on day one to avoid getting in line at each park. Each rental is for the whole day and transfers if park hopping. We have no desire to wrestle with a stroller on the bus. In the AM it usually isn't too bad, but at night when the buses are jam packed, we see people struggling with strollers, baby bags, kids, purchases, etc...not a pleasant thing when exhausted at day's end.
2 yrs. ago we learned that the luggage services at the resorts keep some strollers on hand. They told us people buy inexpensive strollers in FL and then leave them behind when they return home. Disney donates most of the strollers to charity but does keep some for guests to use for free. What we do is check out a stroller from our resorts luggage services. We use it to go from the room to the bus in the AM, check it in at luggage services, which is right by the bus stops anyway. We ride on the bus with our kids (DS 7, DS 2) free of wrestling with strollers. Then when we return at the end of the day, we check the stroller out of luggage and wheel the kids (usually asleep) back to the room.
If you don't mind carrying the strollers on the bus, then you get the advantage of a free stroller the whole time you are there. We just happen to prefer the convenience of the park strollers and thus budget accordingly.
Hope this was helpful.