I have two snakes that I feed in their enclosures with aspen bedding. For some reason those two get freaked out by getting moved into a tub and will not eat.

I just dry the mouse off really good so that no bedding sticks to it and I haven't had a problem yet. Sometime if they are hanging out by their water bowl I will pull the bowl out. I have had them dunk a mouse in the water bowl and straight onto the aspen. Then you have to pick the aspen off while they are eating it. (Not Fun)

Some people will say to never feed on the substrate, some will say they have always done it. In the famous words of BT on reptile radio. Do what works for you!