It's interesting that you say you no longer wake up with a smelly mouth. Mouthbreathing or dry mouth from other conditions causes more bad bacteria to form. Hence, bad bacteria in the mouth can simply be related to a dry mouth. One thing recommended is to chew sugarless gum (mint flavor for breath) to produce more saliva in the mouth. I think taking mouth probitoics before bed can also help such in your case.
It was pointed out if you have white film on your tongue, then you have bad breath. Did you have white film on your tongue? Do you have it now?