What kind of glass can I purchase that will melt in a Bunsen burner flame?
Is there any way to treat glass such that the melting point is lowered? I tried adding some sodium hydroxide but the glass shattered when heated.
There are a few options for low-melting glasses that will easily melt at the temperatures of an air-gas torch (i.e. a Bunsen burner). I suspect that either soda-lime or lead glasses would be the soft glasses of choice for your application (making Prince Rupert's drops).
Soda lime glass should be an adequate choice. For some applications, it can be prone to cracking if not properly annealed, however.
Lead-based glasses are among those with the lowest melting points of any glass, and probably the lowest applicable to your application. Annealing is simple and can just be done with the torch itself. Lead glasses also have a large "soft" temperature range (the range of temperatures below the melting point at which they are still somewhat pliable). This is seen as a disadvantage in many use-cases, where sagging prior to sufficient cooling/hardening is a problem. For your work, I would think this would either be a non-issue or possibly could even expand the possibilities for making cool looking drops ;)
Given the availability and affordability of these solutions, further treatment to reduce the melting point just seems like a waste of good glass-working time.