Shooting with your opposite hand may feel extremely clumsy, and you might think it would take too much effort to become proficient with it. Actually, our brain is pretty capable of switching things over. All your opposite hand needs is a little muscle memory.
Try practicing by running one full rack once a day with the opposite hand. Within just a few days it will feel far more comfortable than when you started. This is a must-have in your arsenal when you come across a shot requiring a bridge, but would be a cinch with the opposite hand.