As LGray said a few small pieces of aspen stuck to the prey item that gets ingested won't hurt you BP. It's rare though that the aspen stuck to the prey makes it into their mouth, it's such a tight fit that most shavings fall off as your BP eats it.
If you do go ahead and start feeding on aspen I would recommend to of course supervise feedings to make sure no big chunks of substrate are stuck to the prey and to keep some kind of deification record to make sure you BP is going regularly and isn't impacted (how much they go depends on how much they eat and how old they are).