Weak Side Rule?!

I have a muscle imbalance between my left and right arms(particularly biceps). I have read about the weak side rule but am wondering about a few things. If doing barbell excercizes is bad, should i cycle the barbell and dumbell work with an emphasis on dumbells? like 3 weeks on dumbells, 1 week on barbell? Has anyone else trained past an imbalance? What did you do?