You have a couple of options, though both require tearing a bit more dry wall out than just for wiring. You can get an electrical box from just about any hardware store that is attached to a cross bar like this:

Or you can span between two studs with your own 2x4 and mount the box to that. That's what I did just recently in our small bathroom for a new vanity light fixture. That seems to me as the most secure.

I suppose you could use wall anchors. You can buy some that are rated for well over 100lbs these days. Even so, that doesn't strike me as code, however. Certainly not the safest. At least, not without the box.

I would love to hear other people's thoughts.

Joe