I have not been on the gondola [Hells Gate] which takes you over the river at an extremely narrowgap.
Your bus looks to have about 140" wheelbase or so... so getting into camping at provincial parks is easy, but the outback stuff would be hit and miss. This is a very low population and tolerant area, though.
Visiting - BC Parks - Province of British Columbia
If you are not in a rush, there is a campground at nahatlatch lake, [cross the bridge at Boston Bar] but it would be an in-and-out road, no loop available for a bus. Another nice park is at skihist, out of lytton, but if you are really rolling it might show up too soon in the day. If you take 12 to lillooet, and then 99 toward Clinton, there is a campground on the way to Clinton.
The Gang ranch is out there, a long drive with a beautiful old suspension bridge across the Fraser, and very historic, but the ranch itself is not much to look at. It would be pretty easy to spend a month in the general vicinity.
Lots of stuff to explore in the area, but I am not used to thinking "bus".
You are no doubt set up with fuel and tire patch gear and would be okay that way on the gravel roads, but quite a few roads deteriorate and become un-bussable many miles out. Inquire locally is the tactic, sometimes you have to talk to several people to get the real dope on a route.
These are decent atlases:
British Columbia : Backroad Mapbooks, Recreation maps, GPS maps, Topo maps, Fishing maps, Digital maps for BC, Alberta, Manitoba, Ontario, Nova Scotia, New Brunswick, Canada
You can't take bear spray across the border, but compressed air boat horns may be handy if you decide to camp out in the sticks.