All I can tell you is based on my own personal experience. We feed 30+ snakes here every week, from little hatchling ball pythons to big mature ones, to boas to a milksnake. All in their enclosures, all on a variety of substrates that range from newspaper to aspen to an aspen/cypress mulch mixture.
If feeding in the enclosure or feeding live caused a snake to bite you, well I'd be pretty much chewed to pieces. I'm not.
Their digestive acids break down fur, teeth and bone completely - a bit of fine shred aspen isn't going to create an issue. If they get a bit stuck in their mouth they can usually dislodge it, if not then you can pull it out with a pair of tweezers. If you're concerned about loose bedding then a few hours before feeding time you can always lay down a big square of newspaper over the area of the enclosure your snake is feeding in. Leave it there until the next morning or at least a few hours later so you don't accidentally get nipped by a still hyped up, just had it's dinner snake.
I would suggest though that on future feeding days that you keep handling the snake to a minimum, especially handing it around for someone else to handle too. These snakes get to know what day you feed on and can become very hyper sensitive on their feeding day. Too much handling that day can get you bit or the snake so freaked out that it then refuses to feed that night. Just a thought....