It depends on what you would like to sterilize. Bunsen burner can only be used to sterilize metal loops, glass rods and mouths of glassware. But it is not useful to give extra sterility in your bio-safety cabinet if you just keep one. I hope you got my point.
In fact I need to sterile the mouths of glassware even though its already been DHS and autoclaved. But thing is that what is the feasibility to work with burner into a BSC. Is the really help or increase the chance of accident.?
The only thing you need to take care of is to make sure that the flame stays all the time if the gas is on. Accidents may happen if you turn on the gas and leave it without lighting it. This is because, the air pumps of the hood sometimes generate sparks which can lead to flames in case of gas leakage. The same can happen with excess use of ethanol. I hope it helps. Goodluck.
DO NOT operate a bunsen burner inside a biosafety cabinet. This goes against safe laboratory practices. The open flame can lead to an explosion. If you want to use the burner, use it outside the cabinet.