You are correct that there is a wheelchair vehicle for the Safari. The front seat has a spot for the wheelchair and is tied down, similar to the tiedown straps used for Toy Story Midway Mania. There is a bench seat where one or 2 people can sit next to the wheelchair and another similar bench seat in front of the other.
I've got pictures of it, but not posted online yet.
TSMM is a different type of bumpy because it's sort of whipping you into a circle, the movement is quick and you know when it is happening.
The Safari is bumpy, but how bumpy depends on exactly which bumps the driver hits. So, one ride may be more or less bumpy than the one before. There are no sudden or sharp turns and no way to anticipate most of the bumps.
The speed during most of the ride is quite slow.
That said, it's like driving over a country gravel road with some potholes; not constantly bumpy. There is a bridge at one point that rocks and moves as if it may fall down - this feature is not operating on every ride, o you are not sure whether you will get it or not.
That is probably the most concentrated bumpy part. If you have been on the Backstage Tour at the Studio, the ride car is fairly similar. That part of the backstage tour is bumpier then anything on the Safari.
The Safari is one of my daughter's favorite rides, but she likes bumping. She is very secure in her wheelchair and has good head control.
