Would it be possible to go from a 36H in chest size to at least a B cup?

Congratulations on your decision to proceed with breast reduction surgery; it is one of the most patient pleasing operations we perform.
 
Yes, it is possible to reduce the breasts size very significantly. The concern with the amount of tissue removed is related to blood flow to the remaining tissue; if too much tissue is removed in one operation the blood flow to the remaining tissue (including nipple/areola) may be compromised. Part of the tissue that is left in place is called the “pedicle"; this segment of tissue is responsible for delivering the blood supply to the nipple/areola tissue. If the pedicle is made too small (in the effort to reduce the breasts as much as possible) then patient will likely have problems with tissue survival. 
My best suggestion: when the time is right, seek consultation with board-certified plastic surgeons who can demonstrate significant experience achieving the types of outcomes you will be pleased with. This careful selection of plastic surgeon will be the most important decision you make.
Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. For example, a “B cup” may mean different things to different people and therefore may be a source of miscommunication. In my practice, I ask patients to communicate their goals with the help of goal photographs.Most patients wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso.   
I hope this helps.  Best wishes.

Dear Beautiful3771,
breast reduction is best suited for women who wish to decrease the size of their breasts. While there are different techniques used to perform this surgery, I prefer the vertical incision (lollipop pattern) breast reduction technique instead of the anchor scar pattern, which reduces more noticeable scarring than usual. I also use a SAFE liposuction technique to reduce additional fat around the stubborn axilla area and bra line. This way, my patients are achieving beautiful results with minimal incisions which reduces downtime and delivers an overall better breast shape long term.If you are considering breast reduction surgery, you should consult with a board certified plastic surgeon to discuss your options and make sure your surgeon understands your goals. Only after a thorough examination you will get more information and recommendations.
Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery