Small pieces of skin and other human or pet body substances are common on bathroom surfaces and that is what your dermestid larvae are feeding on.

Where would they be "hiding?" Do I have to worry about them getting to other parts of the house? Is throwing out that bath mat enough? Thanks

FOund another this morning crawling on the tile floor. Again, just one. No sign of them anywhere else. COuld they be in the walls? Coming from a neighbor's apartment?

I doubt they are surviving on the mat alone. They only need a millimeter crack to come and go. Research dermestid+control for ideas. Keep an eye on any natural fibers or oily/fatty/starchy food items.

Just wash it. Don't toss it. If they are only in the bathroom, give the bathroom a thorough deep cleaning. Wipe everything down. Launder everything launderable.

The odds are good that ONE adult beetle flew in somehow and laid ONE batch eggs and now you're seeing the ONE batch of babies. They probably are half-starved and not very healthy anyway. You should be able to wipe them out in one cleaning frenzy.

Everybody gets these guys. It's not a big deal, honest! :)

Tossed the rug. Actually, we are moving out of here in 2 weeks, so tossing lots of stuff anyway - no room in new place - downsizing. Since yesterday, so far, I have not seen any new ones. Had concern baout bringing them to new place, but there's nothing from that area of the house that we are bringing. Unless they travel long distances & could be in some boxes?

They probably live where you're going too. You might get fresh ones.