Hi. I'm 25 years old, 4'11 feet, 110 pounds, and a 34dd breast size. I want to have a breast reduction to a B cup.

At
size 34 each 100 grams of tissue corresponds to 1 cup size change. To go from a DD to a B would require 300
grams removal. Insurance companies may
not authorize removal of this small amount desired. Size B may look disproportionately small on
you. I recommend a new technique called
The Ultimate Breast ReductionTM.
This technique avoids the ugly vertical scars of the Wise pattern,
maintains nipple sensation and the ability to breast feed. Your breast tissue is reshaped creating upper
pole fullness, elevated higher on the chest wall and more medial to increase
your cleavage. The weight of the breast
is transferred to the underlying muscle resulting in immediate pain relief
without excessive reduction. This allows
you to choose the size proportionate to your body.Best Wishes,Gary Horndeski, M.D.

 Based on your description you may be an excellent candidate for breast reduction surgery  at some point; it will be in your best interests to drop weight first.  Doing so will help decrease the risks of surgery and help minimize the chances that additional surgery will be come necessary in the event of weight loss that occurs after the breast reduction procedure.
The best way to obtain insurance coverage for breast reduction surgery involves some “hoops” to jump through. The more documentation you have (for example, from your primary care doctor, physical therapist, chiropractor etc.) the better when it comes to obtaining insurance “authorization” for the procedure.
This documentation and letter/pictures from your plastic surgeon will help you obtain authorization. Make sure you are  consulting with a well-trained/experienced board-certified plastic surgeons.
 When dealing with health insurance companies, be prepared to be persistent. Keep in mind, that breast reduction surgery tends to be one of the most patient pleasing operations performed.
I would also suggest that you communicate your goals clearly with your plastic surgeon and make sure that you have realistic expectations prior to proceeding with any type of surgery. In regards to breast size desired, also communicate carefully. In my practice the use of goal pictures are helpful in this regard; a discussion of cup size can be confusing and imprecise.   Therefore, I would not suggest that you communicate your goals and/or base your satisfaction with the outcome of surgery on achieving a specific cup size.
 I also find that the use of pictures is more helpful than the words “natural” or "proportionate” etc., which can mean different things to different people.
Many of my patients choose to have enough breast tissue removed to help alleviate symptoms while retaining enough breast tissue to remain proportionate to the remainder of  bare torso. Again, preoperative communication will be critical.
 
I hope this, and the attached link, helps.
 

What you are asking for is certainly reasonable. To get all your questions answered I would suggest seeing a board certified plastic surgeon.to have a full discussion about your wishes and the pros and cons of breast reduction surgery.