As I mentioned in another thread, I tossed into the dryer a bathmat I’d not washed for WAY too long without washing it first.
It dusted the clothes within, not to mention the lint and some places in the rim of the door, with this sand/grain/dust-like substance. Any idea what it is? Does it have anything to do with the three little bugs I found in a place where I had the bathmat for a while (though they could also have gotten in from other objects there)? I hope not! 
Do you mean a fabric bathmat or a rubber (or rubber-backed) one? If the latter, it’s probably the backing disintegrating.
Does the mat have a latex non-slip backing? If so, dryer heat will cause it to disintegrate, and that’s what it looks like when it does.
ETA: Colophon beat me to it!
Any time I put bathmats or door mats in the dryer (even after washing them), I always get that. I always assumed it was just dirt and sand from my shoes.
Ahhhh, that makes sense. It indeed has the backing.
I guess I shouldn’t put it in the dryer anymore; I completely forgot that I hadn’t done so the last time I washed it. Will this disintegration hamper the backing’s ability to, uh, not slip? It was in for over half an hour.
Maybe, maybe not, but in my experience once they start to disintegrate they tend to keep shedding the dust.
If I were you I’d splash out on a new bathmat.
ETA: Best place for it, of course 
Generally, air dry bathmats - but hell, it’s not like they’re expensive.