staying cool/hydrated:
A "cool shirt" is used in auto racing sometimes by guys with more money and less willingness to sweat than me. Good ones cost around 500 bucks and up, but they are SFI certified (to be fire resistant and such). If someone makes a version for applications other than racing, they would be much cheaper. I assume the certification expires and expired ones might be picked up for pennies on the dollar. Nascar surplus is also a way to get neat stuff cheap. The big teams use many things for one race and replace it because so much money is riding on the race that they don't want to risk a failure (I bought an $800 alternator for $35 and it still works great after many years, plus many more things). Someone with more patience than me could also make their own.
Modifying a "cool shirt" might be an idea for some. It's a shirt with capillary tubing stitched into it, a pump, and an ice chest. The thing pumps/recirculates water from the cooler. A smaller cooler rigged as a backpack might make it useful on a bee suit (a tether to a big cooler seems like it would just get in the way).
On the simpler side, I made a Humpty Dumpty costume for a kid to wear in a play. The egg was styrofoam and used a CPU fan in the middle of the back which ran off AA batteries and a switch imbedded in the chest. Kid was in the thing 2 hours a day for a week and ran the batteries down once after the first day because he forgot to turn it off. Solved that by adding a thermostat and the batteries lasted the rest of the week. Same thing could be done with a bee suit with the addition of a standoff cage in the bee suit between the shoulder blades and cutting an intake in the suit. The irritating little bugger still had to drink a lot of water, though.