Firstly, to the woe of those into both pee and bee, bees do not pee. Insects entirely lack kidneys, bladders, livers, and more.
To the question do bees fart, and if they do, is it an extremely dirty fart at that? Well, lets first discuss bee poop. bees mostly use everything when making honey, which is basically pure energy and nutrients. Bee poop is mostly undigested pollen grains and more complex sugars. A bee could poop in your ice cream, and you would be none the wiser. you might even like, it better, for reasons ranging from "culinary" to sexual. Bees are surprisingly clean creatures, and despite bee poop basically being failed candy, bees always leave the hive to poop, they do not poop inside the hive. As for the farting part, any animal could potentially have air trapped inside it, and therefore must expel it, however farting as we know it is much more than that. A bee would not "fart", and if they did, it would be more akin to a floral perfume than a burst of sulfur and feces.

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Again, thanks for giving me Portal. I owe you one.