If you want to come to Bozeman for other reasons and just hunt nearby - no worries, have fun and it will be a great experience. But, please heed the advice in the previous posts. Bozeman is the transplant hunter hot spot and the Bridgers always have a lot of people at every public access point, even the crazy people who didn't transplant here!
If I'm interpreting your user name right "PA" backwoodsman, and you're driving from PA, you might consider hunting the Judiths, Snowies, Pryors or Little Belt mountains. All of those might even be a slightly shorter drive.
A few hours away from Bozeman and your chances of seeing and getting a bear will be way better.
As far as access to any public land black bear hunting, at that time of year much of it will be based on weather. Roads to trailheads could be, and will likely be, completely clear or they may covered with snow and impassable. No matter if the weather is terrible, there are always places to access public land, like along the road from Bozeman to West Yellowstone for the Gallatin and Spanish Peaks.
No matter where you go, please post pics of your trip!