Bartholin Cysts

Drainage (either surgical, laser or via a catheter) are the only treatments I know of for bartholin cysts.

As far as natural treatments go, I don't know of any. 

However, if it was me, and the cysts were problematic (large or painful), and I wanted to give natural treatments a whirl before undergoing conventional medical treatment, then I would try the homeopathic remedies Silica and Pulsatilla to see if they would help drain the cyst.  Best case scenario:  the cyst resolves after taking these remedies.  Worst case scenario:  no change.