Best forum for Utah beta is Utah Rivers
Not familiar with "Bear Canyon". Below Deer Creek to Vivian park is a popular class I-II beginner/tuber run good for learning or for working on basic skills like catching eddies or rolling in moving water. I wouldn't say there's whitewater besides a few little waves, a tricky bridge trestle to avoid, and a few rocks and avoidable underwater logs placed for trout habitat. Runs almost all summer.
Below that is Bridal Veil section. Fun, class III-IV-, with potential for cold long swims if you're not up to it. Only runs for a few weeks each year (a month on a good year), late May & June. Follow the utrivers forum and you'll know if its running.
If you're asking about the upper Provo Falls/Slate Gorge class V section, I don't have any beta for you.