Yellow sticky traps can be helpful. Also, if you can find a source, there is a parasitic nematode, Steinernema feltiae, that targets the gnat larvae. It enters the larvae through body openings (mouth, breathing pores, anus) and emits a bacterium that ingests the "stuffins". The larvae usually die off within 3 days or so. I'm also aware that there are granules that many people sprinkle to control outbreaks but I am not sure if your Bear could get into those?
