I have a spot that was burned around 2007 that is still very productive for bears...just getting damn hard to see them in a lot of spots in there. Ideally 1-5 years for the sake of visibility but depending on the vegetation burns can be bear magnets for a long time.
Natural burns typically happen in summer/early fall. I would say as long as the fire wasn't too intense then by the following spring it should be more productive than before, although over the years more and more bears will get used to targeting it as a spring/summer food source. Sweet spot in my opinion would be 2-4 years.