I can't for the life of my get my bp to eat outside his enclosure. He's a picky eater when I pre-scent, wait till midnight, and sneak up so he doesn't see me. He's just that picky! Also when you get a few snakes it becomes a hassle to remove to a separate feeding enclosure.
And I agree, your hands should not be associated with feeding. Get Tongs!!!
I feed in their cages but keep tongs handy to pull any bedding off the rodent or out of their mouth. To the OP: in the future when you see your ball pick up a piece of bedding you should try to take it away from him/her don't just watch them eat it. That being said I hope your BP digests it just fine, I've had snakes swallow bits before with no issue, no big pieces though so I wish you luck.