I'm assuming that you're not putting the pieces inside the vase if you intend that it be used for flowers? If I understand you correctly, you want the person to be able to wash the vase occasionally and not peel off the images?
The best thing I know of is spar varnish, which these days is actually polyurethane; it is meant for waterproofing the deck finish on boats. Several coats of it will let you run a wet sponge over the surface without messing it up. For the best result I would suggest using fine sandpaper on the glass first, to roughen the finish and give the polyurethane a better surface to adhere to.