Are there natural ways to dissolve gallstones?

None: Speak to your doctor, if you have no symptoms could be observed and have pain , fever , jaundice etc will need surgery . Gall bladder removal is a low risk amulatory surgery.

Not really : Weight loss, exercise and some meds may help to disolve stones but it can take months and the meds are expensive. Further, the stones tend to recur when you stop the meds. See nih or mayo clinic website on gallstones. Still, it is important to remember that it is not necessary to remove all gallstones. If you watch your diet and it doesn't hurt you it can be followed without surgery.