In my opinion, water changes will be the best thing for you to do about the bacterial bloom. They occur in your tank when there are too many nutrients in the water to support the bacteria, in this case, not the bacteria you are looking to keep around. The best thing to do is remove the food from the water that these bacteria need to thrive. Make sure that you are not over feeding your fish and do regular substrate cleaning with a siphon vaccum. The less decaying food and organic matter in your tank, the better. This is going to be somewhat hard for you to do though since you are fishy cycling so you may have to wait it out.
Without having a test kit right now, I would do water changes very frequently to avoid hurting your firemouth or having it die from ammonia or nitrtite poisoning. This will also help to keep the bacteria bloom at bay, but will slow down the cycle a little bit because you are removing ammonia and nitrites from the tank that otherwise would be a source of food for good bacteria. It is a give and take sort of thing when cycling with fish so be patient.