I had intolerable side effects on effexor (venlafaxine). Now that I am taking a mood stabilizer, will I be able to tolerate wellbutrin?

Possibly. The two meds are different classes. Each person is different in how each med can affect. As long as your doctor has provided the prescription and you stay in contact/ open communication and feedback, it is worth a try. Good luck.
More than likely yes. Wellbutrin has a very different set of characteristics and side effects when compared to effexor (venlafaxine). However, my first question would have to be what mood stabilizer are you now taking?