While 'bezzle' has long been a term in the East for oral sex, in Akron (particularly the Middlebury and Laird neighborhoods), 'bezzle' has come to mean meth. This definition has only come into use over the past two years, and although origins are unclear, it is thought the name came about from the method that an alarmingly high number of both women and men (see Grace Park) use to obtain the drug.
See also: crystal,meth,speed
I think Liz is on with the bezzle, but she's out of grass.