So after some experimenting on this process we came to the conclusion that if you use a battery powered Dremel, you will probably have great success. The electric Dremels seem to have too much power and can easily break the glass while drilling. The battery Dremel has a control where you can turn down the revolutions to a very slow speed if necessary, thus allowing more hand control and less friction.
You still need to submerge the glass piece in water to keep not only the piece of glass that you are drilling cool but to keep small glass particles from becoming air born, allowing the possibility of being inhaled. Plus we always use diamond drill bits and they need to be used with water so as not to wear the bit out quickly. We start on either the top or bottom side of the piece and continue drilling until the piece is completely drilled through. We do stop from time to time to make sure the piece can cool down since if the piece over-heats, it can break.
A battery powered Dremel is also what we use when cleaning the bead release out of the interior of our soft glass beads (lampwork beads). Once again, we found that we broke beads when using our electric Dremel.
Please keep in mind that it is much safer using a battery powered Dremel around water!
Photos by Harrach Glass