I have over fifty beehives on my place and well over two hundred within flying distance and three humingbird feeders that are visited constantly.
Just make sure that your bird feeders have a deep nozzle on them as the bees will devour any sugar you put out if it's shallow enough for them to drink.
Also, I don't think the birds are scared of bees. They work different flowers because of anatomy as I said above. The birds will collect nectar from trumpet shaped blooms while the bees need a flatter flower that they can access.

I have honey bee hives and am concerned as to wether or not the use of dipel dust in my garden will kill the bees.