Put a hook on it.

The under-the-table bag hook. A simple, little thing that lets the ladies know, “you get it”.  Nothing fancy–just a practical hook (retail price, less than $1) to keep us from having to drape our purses on the backs of our chairs (vulnerable, conspicuous, cumbersome) or setting them on the floor (gross). It’s becoming practice at many places (namely bars and cafes) but not enough.