How to get germs off of paper?
Your best bet would be to laminate the picture at a local print shop.  That would seal whatever has gotten onto the paper behind an impermeable barrier of clean plastic.

Barring that, you can probably get rid of most of the bacteria by exposing your drawing to ultraviolet light.  UV light is used in many industries as a disinfectant.

As for the amount of time that your picture spent on the floor, according to MythBusters, time isn't as important as it appears.