I usually buy them already finished from the thrift store, they usually have a lace edge. If you have a friend or family member that frequents thrift stores ask them to keep an eye out for you! :) They are usually in a pack with cuts of aida.
I haven't worried about stiffness for a bookmark; mine are all floppy and everyone likes them anyway. But I do cover the back with fabric. I pick something that goes with the theme, or something that person would like. I cut it a little bigger than the bookmark, press under the edges, and then sew it down (sometimes by hand, sometimes with sewing machine.
HI. since bookmarks are supposed to be thin and also working aida with another fabric or backing does not come out neat, what I do is cover the bookmark (totally finished of course) with a coat of scotchguard fabric protector, the one they use to cover needlepoint works. If you don't know what it is or where to find it, you can search the web for a local store.