Non-Disney buses, but provided by Mears. Unfortunately, it's been several years since I stayed on HPB (okay, fine - eight years, two months, fourteen days) and I only used the bus a few times - but iirc, they're coach-style and so SHOULD be wheelchair accessible.
Otherwise, yeah, they do have to make alternate arrangements for the guest. A couple of years ago when I stayed at a Travelodge that provided all-park transportation, they ended up getting a wheelchair-accessible taxi for me and paying for it.