I am currently a size 32H, petite, 125 lbs. 5'3". Is it realistic to get to a B cup size and still have the breast look shapely?

In my experience that extent of size reduction is NOT possible.  Breast reduction eligibility and coverage by insurance varies from one insurance carrier to the next, and cannot be determined based on cup size, but only based on an in-person examination to figure out how much tissue the surgeon needs to remove.  You also often have to qualify for multiple other criteria from your insurance carrier, so be sure to request their breast reduction coverage policy ahead of time before your plastic surgery visit to ensure you meet all the other non-size related demands that they have.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search.  

Thank you for the good question and 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. 
 Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. 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 suggest that you do not communicate your goals in terms of achieving a specific cup size. For example, a “B cup” or "shapely" 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.
  It will be important that you feel comfortable that your selected plastic surgeon can demonstrate lots of  experience achieving the types of outcomes that you will be pleased with. Looking at before/after photographs and talking to previous patients would be helpful in this regard. Basically, patients should look at the overall "quality" of the outcomes achieved;  in other words, it will be important that patients see lots of examples of outcomes that they would be pleased with.  In doing so patients will be able to get an idea of each  plastic surgeon's "aesthetic sensibilities". Of course, careful evaluation of the photographs (including factors such as time out of surgery and initial anatomic starting point) will be important as patients evaluate before/after photographs.
 Well experienced plastic surgeon should be able to demonstrate lots of examples of before/after photographs;  if the prospective patient does not like anything he/she sees (when it comes to the quality of the postoperative outcomes), then the plastic surgeon is likely not a "good fit".     In other words, appropriate quantity/quality of before/after photographs may be one of the factors that gives patients confidence that the plastic surgeon they are considering can achieve an outcome that they will be pleased with. Best wishes.

Maintaining excellent aesthetics is a key component of performing a high quality breast reduction.  Technique and experience are paramount, and an in depth discussion with your surgeon will help guide realistic expectations.  It's important to understand that it's difficult to guarantee a specific bra size, rather a general volume to be removed can be determined.  A visit to a plastic surgeon's office will help you to understand if you're a candidate for the procedure, and what aesthetic outcomes are realistic in your particular case.  In order to get a qualified, ethical, and expert opinion on your surgical options and expectations, schedule an in-person office consultation with a plastic surgeon certified by the American Board of Plastic Surgery.
Best of luck,
Keith M. Blechman, MD
New York, NY