There are 7 resorts in the Diwntown area that are on Disney Property, but not owned by Disney. Those are Wyndham, Holiday Inn, Hilton Orlando, Double Tree Suites, Buena Vista Palace, Best Western and B Resort and Spa.
They run their own bus system; not every bus is necessarity accessible, but they are required by the ADA to provide accessible transportation that is comparable to that offered to other guests. So, if you are staying in one of those resorts, discuss your needs with the hotel staff (front desk or concierge).
For WDW Downtown Disney area resorts owned by Disney, it would be rare to encounter a WDW bus that is not accessible. These resorts are Saratoga Springs, Old Key West and Port Orleans (New Orleans and Riverside). These have the same bus service as other WDW resorts.
The entire WDW bus fleet is accessible, so the issue is when it is busy and they have to add additional buses from the Mears bus fleet.
Those are 'tour type' buses with luggage storage underneath. Although some are equipped with wheelchair lifts, they don't use them when they are using the buses for busy times - it's too time consuming to use the lifts and those buses are often not actually in the bus loading spot, but next to it.
As kellykins mentioned, the only time that you are likely to see those buses is when it is really busy; even then, it depends on the resort. It is more likely to happen at one of the larger resorts because they have larger number of guests being transported at the same time.
the bus drivers or transportation coordinators can call an accessible bus if needed or will check to let you know when the next one is expected.