If you intend to use the Gnatrol, you'll need to get rid of the bulbs and water the old fashioned way. At least for a while. Gnatrol has to be used as a soil drench.

Gnatrol has been around for many years as a control for fungus gnat larvae in container crops. When used according to label instructions it should be very effective for you. It is highly unlikely that you can harm your plants even if you don't pay attention to the label.

Does your watering bulb system allow for a drying out period for the soil? If not, that is certainly the root of your problem. In truth, you could still be over watering your plants, bulbs or not, if the soil doesn't get a change to dry out.

Fungus gnats must have a pretty moist environment in order to thrive. Allowing the medium to dry out somewhat between waterings AND changing the medium to one that is very coarse and fast draining will prevent a re-infestation from occurring.

I use a potting mix that is mostly bark. It drains rapidly and does not provide a suitable breeding ground for those pesky fungus gnats.

Anyway, I strongly recommend the use of Gnatrol. With it, and the other suggestions I've made, you should be gnat free!

But only after you disrupt the life cycle. That will require about 3 weeks.

Yes, three or more weeks of regular watering with the Gnatrol solution.

This is "Bacillus thuringgiensis - Isrealanis" a limited action pesticed that must be ingested (eaten) by the target insects and is effective for only a short time in the insects life span, ie. the first weeks of the larvas life.
The single best means of controling these wee buggers is to allow the soil of the plants to dry out between waterings, although people in the business of selling you stuff you usually do not need will tell you otherwise.

Here is a link that might be useful: Fungus Gnat Control