Braden Todd of Glassmith2 covers how to prepare a stone to prevent paint-bleeding. To sum it up:
Properly prep the surface so you don’t have any under-bleed of the paint on the stone. When you’re done, you should have clean letters and designs.
To begin, you want to create a coating on the surface that you put the laser mask on. Use a paintbrush to apply a mixture of water and glue onto the stone. Set the stone aside and let it dry.
The next step is to apply a laser mask to the stone. Press the mask onto the stone and trim off the excess. Try to chase any major air bubbles away from where the design will go. Now your stone is ready to be lasered and then sandcarved.