Oh God, Nature! It's all over me, get it off!! 
a) It's their garden, and they're not breaking any laws.
b) You don't keep bees, bees choose to stay if they want to. (You can lead a swarm to a hive but you cannot make it stay!)
c) Mason bees are non-swarming, non-aggressive and harmless as long as you don't go interfering with them.
And actually you could keep chickens in your garden. A cockerel however is a different matter with regard to noise pollution and anti-social behaviour. And if you're worried about aggressive animals, a cockerel is something I would advise against. Strongly.
You also don't need a special place for them to nest. What exactly would you do if they started living in another neighbours wall? Demand they tear it down??
We don't keep bees, but our early apples are in full bloom at the moment - swathed in beautiful blossom. They're also covered in bees
and I'll wager we have far more flying round our trees than your neighbours have in their little bee-house!
Nature happens, you'll have to get over it, sorry!