if it's really a big worry, feed them outside the tubs. you can also put the prey item (assuming you're feeding prekilled or F/T) on paper towel inside the cage and that minimizes contact with the substrate. if the prey is totally dry bedding doesn't tend to stick to it a whole lot, so that's another option.
i've seen my snake ingest some aspen on a rat before (usually she's fed in a tub but she wasn't eating so i tried it in her tank) and she was just fine, so a small amount of bedding isn't going to do a whole lot of damage. but, she also isn't fed there regularly and that was essentially the only time she's ever ingested bedding, so i don't know about things accumulating over time.
safest way to go is just to feed in seperate tubs.
~jenny
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1.2 normal ball pythons (Cindy, Darwin, and Periscope)
0.0.1 california kingsnake (Tetris)
1.0 rex rat (Scurvy)
1.0 gerbil (Yerbul)
0.1 bunny (Spazz)
1.1 betta fishes (Vicious and Killer)
2.2 great danes (Shasta, Odysseus, Merlot, and Watson)
1.0 fat fuzzy mutt (Smokey)
1.1 cats (Thidwick and Turtle)
2.0 horses (Buddy and Sam)
1.0 goat (Billy Jack)
1.25 chickens (Ugly the rooster and his harem)
"God is a comedian playing to an audience too afraid to laugh." - Voltaire