I've been working as a biochemist for over 25 years. The claim that burners "waft away bacteria" is absurd and I'd worry about the education of anyone who claimed so.

Sterility is (or at least was) usually created using alcohol or bleach. The flame was just for small tools. For example, when plating bacteria you'd wipe down the bench with ethanol or IPA. Sometimes for fun we'd burn the excess off, but that was mostly just for a lab goof. We used metal loops to spread the bacteria on plates, and those got flamed in between samples to clean them, sometimes after dipping them in alcohol. As others have said, nowadays most people use single-use plastic labware to do the same job. Most lab fire safety people ban burners for this type of general work.

[–] AmidFuror@fedia.io 2 points 3 hours ago

In a corporate lab we would use bunsen burners just to ignite the alcohol on a glass spreader before spreading transformed bacteria. I was never a fan of the wire loops, but those would work too since they can cool quickly.

I have never heard a claim that the flame itself sterilized the broader area.

I also used the burner to make the spreaders by melting glass rods to have a triangle-shaped head. Those were fun times.

Edit: We also used to flame the head and necks of a flask before putting a sterile pipette inside. I guess that was to kill bugs lingering on the outside surfaces near the opening.