Like I said, I don't have bubble experience, but I consider myself a good researcher and have dealt with a few other nasty bug problems. I would assume clean the Rez and treat the new water. Dont think there are proportions on how to use that Bayer in a Rez, but I know it's been done, you can probably find someone who has done it before. It's my understanding u need to dip the plants every other day for 2 weeks, the reproductive cycle is like every 3 days. After u dip, let the insecticide do it's business for at least an hour before kicking the bubblers back on. The most recommended treatment by far ive seen is Azamax if u want to venture out.
I've dealt with a couple other infestations including mites and gnats, and I always found that a multi pronged attack worked best for me. Find the best several options and just do em all. A good chemical, a good organic, a good foliar spray or 2 like an insecticide soap, and some sticky traps to to kiill a couple extra but even better see your progress. Pretty much my main concern when spreading poisons around is not to kill my dog. That tree and shrub is probably the right stuff if home depot is your only option, just gotta get ahead of those fuckers you should be good.