A proper thing to do might be to report the bike as found to the cops and give them a serial no. Ask if anyone's reported a bike stolen and let them know that you'll be keeping it if you don't hear from them or an owner in 30 days.

I once left a neat dutch-style bike, a beater with lots of different issues, out on the sidewalk, leaned up against a building. In Boston. It stayed there a full 3-1/2 weeks before it finally walked away.