Yes, I’ve given my bunny some of the flowers along with the greens. She loves her fresh dandelions. We have bird feeders, too; not dozens, but a few, and they’re always well-stocked. You really shouldn’t have to worry about the birds as long as there aren’t swarms of them and you wash the greens you pick thoroughly. Usually bird diseases are spread to other birds when bacteria in their droppings contaminates bird seed at feeders. It’s almost always a bird to bird issue as far as I know. We also have ground hogs, deer, cottontails, chipmunks, squirrels, dogs, and cats running through our yard regularly. I just kind of expect it, especially during the spring. I think it’d be highly unusual for a pet bunny to get sick from eating dandelions that have merely been exposed to other animals. Carefully washing anything you pick should prevent any potential problems. Personally, I am more comfortable giving my bunny stuff from my yard or stuff that I am growing as opposed to giving her stuff from the grocery store, since I don’t know the circumstances associated with how that produce was treated before it got there.