I haven't tried this but you could get some mosquito netting and make a hood out of it, and just make it big enough to cover your helmet (if you are a helmet-wearer). What I'm thinking is the sort of stuff that camping tent "windows" are made from. It'd look funny but it wouldn't restrict breathing and you wouldn't eat any more bugs.
Not with the bee thing, but a few years ago I was out on a jog and a bug flew in my mouth and down my throat. Couldn't get it down, couldn't get it out. Ended up gagging and throwing up, I'll bet that looked good to the other people on the track at the time.