How to stop invisible, mouths eating my herbs, basil

Most likely slugs....Apply food grade diatomaceous earth,a tray with beer,wrap around a cooper flashing,and apply a horticutral oil.

Seeing your in Texas not sure it would be slugs - I lived here for years and still haven't had slug issues in my garden. Get some ladybugs from the nursery and set them free in your herb garden - they may be able to help remove the issue. Welcoming nature into the garden is a great way to detour bugs, especially the ones you can't see.

I would agree, most likely slugs or snails. Do you see a slimy trail around the plants? If you do, get a product to kill them.

BITES? You can see where it's bitten? Chances are it's a critter. Bunnies, squirrels and voles will eat stuff if they are hungry enough.