I saw somebody do something very similar a few years ago. They formed a New Mexico corporation (why NM? I don't know). He registered the bus at the mailing address of the corporation and called himself a part time employee that drove the bus in the US.
I know that he did take the bus, temporarily, into Canada a few times and he did have some rough spots doing it.
I have taken converted buses, 5th wheel trailers, passenger vehicles and smaller commercial vehicles in & out of Canada a number of times. As a rule, I avoid the process if I can. The folks at the border generally give me the impression that they would prefer that I stay home....
If you are set on the idea, I would look into forming a corporation in NM, NV or SD. I don't know which is the "popular" one right now but there is plenty of info out there.
https://www.myllc.com/which-state-to-form-llc.aspx