Hi Lisa,
Generally speaking the food should be no bigger around than the snake. I think most would agree that a mouse slightly smaller around than your snake would be just fine. BP's are active at night and therefore should be fed at night. And yes, just drop it in. Keep an eye on things though. If your snake doesn't strike soon she is probably not hungry, or stressed. Wait a week and try again. Just don't leave live food in with the snake unattended. Hope this helps.