You can feed your snake in the enclosure, Aspen Bedding will not harm your snake at all. I feed my colubrids and my boa in their cage and they have Aspen. Not one of them as ever been impacted. I've had this one King snake for 3-4 years now and he's never been impacted from swallowing some Aspen. You'll be just fine feeding your snake in the enclosure, but if you don't feel comfortable with it then you can feed in a separate container.
I feed my BPs in a separate container, just because I don't know if it's really safe for them to swallow Cypress Mulch. So, I just feed my BPs in containers to be on the safe side in case something were to happen.