Holly takes great pleasure in snapping at insects - even bees. I try to prevent this but, am not always successful. Living in a semi-rural environment, we have a lot of bees flying around. It doesn't seem that she has been hurt by the bee stings (I am sure that she has caught one or two). We had a Maltese (of course that is a dog 1/10 or less the size of a doodle) who went into shock after being stung by a bee. We immediately gave her liquid Benadryl and rushed her to the vet and she recovered.
However, like I said, the bees don't seem to trouble Holly at all.
Thule and Cass are quite the fly hunters! They don't give up. However, once I watched Thule lie down and enjoy the show of a fluttering moth on the ground. The moth couldn't get up and Thule just watched with interest. Rosco tried to pick up a fly in the window (makes it sound like my house is full of insects!) but he kept grimacing when it buzzed against his lips and he never did take it.