Yes, they do. You likely will not see most female bees sleeping, as they will return to the nest, which would usually be concealed underground. However, you can often find male bees and other types of wasps sleeping on stems or leaves at dusk and/or dawn. They will usually bite the stem with their mandibles, and just hang there for the night.

Ammophila wasp biting stem with its mandibles.

 

Sleepy Bombus huntii bees.

Other species will sleep in or on flowers. These individuals would be visually inactive, with reduced respiratory rates – remember that insects are ectothermic (“cold-blooded”) and their body temperature, thus activity, is largely dictated by external heat sources. These insects were easy to photograph, and even capture, because they were “sleeping”, and not responding to my presence the way a “non-sleeping” insect would.

Wake up time for the Bombus huntii bees.