You also can think about using a sous vide heater to keep the temp stable during mash.
I also do BIAB with a gas burner.
The burner is to bring everything up to temp, quickly (and for boil, later).
Then, in goes the sous vide to maintain the temp over the hour or so for mashing.
Very easy, although you do need a nearby outlet (or long extension cord).
Also, you have to be able to set the height (not too high, so it heats and recirculates) and not too deep (so as not to fry the electronics).
I set mine in a stainless hop spider that hands on the side of the kettle.
My go to:
Instant Accu Slim Sous Vide Immersion Circulator
It costs about $90.
Easy to use, easy to clean.
About a dozen brews with it, so far, and not a single issue.
Cheers,
Michael