I've messed with this a bit using different products. In the end what mattered most was the brand and the type of paint the used. Some came off fairly easily with an acid soak (Starsan or muriatic acid) and some needed acetone. Some of them work best with a razor scrape after the soak.
Irregardless, almost all of the bottles has a faint outline of the painted areas remaining in the glass. Sometimes it was nearly impossible to see unless you held it up to the light just right and sometimes it was still pretty annoyingly easy to see.