I think before treatment it would be prudent to figure out whether this is really a bacterial infection that he's got. Often after being medicated, fish can become vulnerable to a fungal infection called saprolegnia, it can look like some bacterial infections, but it is much less invasive, moves more slowly, and is treated differently. Often it looks like little grayish tufts, especially on the fins. You might want to google a few images of it to see if it is consistent with what your fish has.
I have used JFE before a long time ago, but have since come to the conclusion that it is a weak medication, so I prefer medications like Maracyn and Triple Sulfa. Anyway, if your 3 gallon has a filter, then you should really choose a different hospital container to treat him in. The medication will ruin your bacterial colony if your tank is cycled, so you should avoid using your regular tank for treatments like this. Rubbermaid/sterilite plastic storage bins make excellent hospital tanks since they are cheap, (about $3) durable, and they're long and shallow so the betta still has plenty of swimming space but doesn't have to struggle to reach the surface to breathe.
The way I think I used it was to fill my hospital tank with about 25% old water from the betta's tank, 75% fresh dechlorinated water and mixed in the appropriate amount of medication, then I acclimated the fish to the new water. Keep in mind that you still need to do water changes as necessary if the tank is small-since mine was two gallons, I did a 100% water change in the middle of the treatment and added another dose.
JFE is an antibiotic, so there are risks involved with using it. I suggest reading this article so you understand how antibiotics work and some of the risks involved with their use: http://edis.ifas.ufl.edu/fa084