How long will I extend my lifespan if I have bariatric surgery?

A good amount. Although I'm sure the exact data for which you're looking isn't out there, we know that obesity shortens the lifespan so we could infer that losing weight, surgically or otherwise, will reduce this shortening, if you will.
Years and quality. Additional years depends on bmi and current age. If 20 years old now and bmi over 50 (about 150lb overweight) then can expect a 20 year life prolongation. But quality of life is also very much improved.
Several years. We know by being obese a person can shorten their lifespan by over 20 years. Successful weight loss surgery can reverse that.