I have a large pot of basil growing in my yard. The other day, I was cutting leaves for pesto, the first few minutes were ok, then a small black and silver (grey?) bee-like insect accompanied me (like it was overseeing my work). Within a few minutes there must have been about 20 of them flying around, landing on stems I had cut, as if inspecting the damage I caused. I finally left when two wasps joined them (unrelated To the "bees," but I'm deathly afraid of them). The "bees" didn't seem to be bothered by me, rather the work I was doing. Any ideas on what they might be?
I doubt the 'bees' were going to harm your basil. More likely, they were attracted to the juice at the ends of the cut stems. If that's the case, they were probably one of the solitary living bees/flies that subsists on nectar, and was getting a quick drink of juice. I've seen this on grape-vines, but it can happen to other plants as well.
This doesn't harm the plant, unless the flies were on a diseased basil plant recently (unlikely). I would leave them alone, and they should leave when the cut stems dry over.
My guess as to the flies themselves is some sort of adult root maggot. See pic below, and let me know if that's not it: