That's what I do. During the trip, I keep it in the plastic package it came in, especially if I'm just in one place for a few days, then throw it away at the end of the trip. Especially if not moving between hotels on a single trip, this also prevents a wet toothbrush from getting other toiletries wet.

At first I though this was wasteful, but then I decided that one of the reasons I work is to be able to have "luxuries" like a fresh toothbrush for each trip, and it doesn't really cost all that much in the big scheme of things.