I wear a full body mosquito net that is very light, and includs a cap with netting for the face. Underneath, I just wear my running shoes, short pants, and a t-shirt. The net lets through plenty of air for cooling and I rarely get bit. It does get hotter than without the netting, though. The hands and ankles are the only vulnerable places. I've spend hours in the Laurentian forest just north of Montreal in mid-May (the peak of bug activity in those woods). Looks funny but it works great. I bought the netting at a camping supply store. I was there just yesterday and the bug activity has dropped so much at this point in the summer than no net was needed. I'm not sure how the netting would deal with bees, as the major culprits here are mosquitos.
Maybe there is a market for integrating a dark cloth with bug netting