How long for a bartholin's cyct to drain?

Not predictable: When Bartholin's glands are draining normally, no swelling/symptoms, thus people ignore. Your question implies a problem in which normal drainage has not occurred, a gland has become swollen, infected & sore. If it does not drain, then a progressively enlarging abscess may result. If it ruptures, or is lanced, releasing the infection & wbcs, +/- antibiotics, then problem will usually decline rapidly.

Quick for a few : Minutes.Don't worry. Take care !

Varies : Some drain spontaeously some do not and need to be surgically drained.