Is offering to work for free a bad idea for an undergrad researcher?
If you are a student who is getting something of (educational) value out of your research, and don't need the money, it's not necessarily a bad idea to do undergrad research without getting paid for it. (If you weren't a student, this would probably be a very bad idea, though.)

Personally, however, I will only supervise students who are either getting paid or getting some kind of independent study credit. (I'm not the only supervisor I know with this policy.) I don't want to put time and effort into supervising a student who is only very loosely committed to the research project.

I encourage you to consider that option - independent study or thesis credit - for undergraduate research.