Exceeding the recommended dose is never a good idea, nor repeating it if it wasn't effective. Most of the insects that Bug B Gone would target are native to your lawn anyway.

(As a sidenote, I'm not a fan of destroying insect life in your lawn. Most of it has no interest in nibbling on you, and much of it is micro-arthropods in the soil that process organic material back into the ground for you--you just killed those off and restoring them will take some time).

There's no effective way to abolish mosquitoes, midges, or most other biting insects from your lawn. They're entirely capable of flying from location to location as their food source (humans and other animals) move around.

My suggestion is that you never use (or misuse) any more pesticides, ever.

The only way to avoid getting "eat up" by insects is to slather your self with repellent. What kinds of insects are they? Depending upon what they are, there might be cultural things you can do.

I agree with leaving bugs alone unless they are destroying something. Bugs which destroy stuff include carpenter ants, termites, chinch bugs, leaf cutter ants, fire ants, crazy ants, aphids, sod webworms, and certain grubs. But if all you have is cockroaches, flies, beetles, pill bugs, praying mantis, ladybugs, earwigs, and other normal wildlife bugs, leave them alone. There are a few nuisance bugs, including fleas and ticks, which you might want to treat for, but I would still not use a non selective chemical insecticide.

You might want to look online for Guardian Beneficial Nematodes. These beneficial nematodes carry an insect disease which kills many insects within a day or two.

It is, perhaps, odd of me, but I'll tolerate sod webworms in small numbers, along with aphids. The webworms don't do enough damage in small numbers to be worth the punch I'd have to give the rest of the insect community to get rid of them (and I find the little fluttering adults amusing).

I've never actually seen webworms get to large enough numbers to cause a problem. Hunters always seem to control the population all by themselves.

Aphids in reasonable numbers are unable to do much damage to plants, and supply a food source to attract ladybugs to my gardens. I like ladybugs.

In larger numbers, aphids control well with simple soapy water, so they're a trivial problem anyway. I regularly inject soap through my fertigation system, so aphid issues are pretty much zero.