1- add mutagens in the media and grow the bacteria, or use UV. Mutations will appear everywhere and maybe in your protein. If you know more about your protein and what kind of mutation you want, you can try to devise a selection step to weed the different mutants out.

2- Sequence the protein. expensive, needs specialized material, but doable…

3- Chop up the DNA of your bacteria in big pieces, clone and look which clone has the protein. Purify vector and chop in smaller pieces repeat until you either do not get the protein anymore, or the fragment is reasonably small for sequence

simply sequence your protein. Nowadays it’s not so complicated, especially with so many sequenced genomes, which should be able to help you find some homologues.
After you get the protein sequence, find the DNA sequence, here you have several choices. And then you have plenty ways to make mutated protein…