Imagine! You've been stuck inside all winter. There's been a bit of cleaning to do, but not much else. The weather outside is terrible. You can't go out.
And then, it's spring. The door is open. Out you go!
The toilet is outside.
And what do you think is the first thing you might do?
Yep. Have a poop. After holding on all winter.
Bees keep their hives clean and make sure they do their business outside the hive. The ones that stay in, queen, larvae and drones have their feces cleaned by the workers. The only time bees might defecate inside the hive is when they have eaten something that disagrees with them like overripe fruit, or they have a disease like Nosema. And then they gotta go when they gotta go. Neither is a good sign.
Winter bees will hold their poop until it has warmed up enough for a short cleansing flight. They will go a bit away from the hive, but not far, maybe up to 500m. They'd be busting, I would imagine. Especially in early spring.
And what is their poop like? Sticky and yellow, and very hard to get off things. Not to be confused with honey. Bees typically fly in set flight paths between hive and food source. If you live close to a hive, and on the bee highway, you will likely know exactly what bee droppings look like, as they cover everything. It will be more of a problem from spring to summer, when the bee numbers are at their greatest, and all the bees are out foraging. During this time they are also rearing brood and cleaning the hive regularly.
The droppings are pretty hard to remove too. But you can try soaking the bombed area with water, keep it wet for about 20 minutes, and then wash with soapy water or a pressure hose. Unless it is your washing, in which case, hang your clothes under cover, or out at night only?
Or you can console yourself that it's a sign of healthy bees and is all natural and organic, and all is well.
And if it really really bothers you, you can ask the beekeeper to turn the hives entrances away from your place, which may or may not work. Although, with any luck, you might get a 'sweetener'. Or long term, plant some tall-growing trees in the flight path, between you and the hives, and eventually the bees will fly around, not over, your house.