new microbiology lab
What're the entry requirements for your lab? If you're working in BSL-2 or greater, the appropriate PPE ensemble is listed and required at all times while you're in there. Likewise, gloves are required whenever you're in contact with potentially infectious materials (OSHA 29CFR1910.1030). There shouldn't be leeway to decide when and when not to wear your PPE ensemble.
As bunsen burners do present a burn hazard, your work with a bunsen burner should be preceded by general lab safety training, and subject to work practice controls. It's safe to wear nitrile gloves working with an open flame, and your gloves are not readily combustible. Burns will typically result from a failure to exercise universal precaution and/or use the burner properly.
If you're working dangerously close to an open flame or with heated materials, consider controlling for injury with thermal gloves, tongs, or engineer out the burner with a biosafety cabinet.