Do you want to go touring or experience famous mountain biking destinations?
If you want the latter, would your budget cover flying between locations in the month? You could pick 4 locations with good flight connections and transfers and spend a week in each. You could ride in a lot of the US and Canada if you were able to fly between cities. Or do a whistle stop tour. You could manage Sun Valley, Park City, Bend, somewhere in Washington then to Canada, Rockies and the costal mountains.
Do some research to see which locations could entertain you for a week. As I’m sure you know, the problem with doing road trips in North America is the size of the place. Unless you want to be driving and not riding, you are better off flying. It takes 12 hours to drive from Calgary to Vancouver, for example. You would pass through some very good places to ride your bike, though. Hiring a car big enough for bikes cN be expensive, too.
No matter what you end up doing, it is going to be fun. I’m jealous.