Is It a Realistic to Want to Go from a 40DDD to at Least a B Cup Size?

Usually it's reasonable to go from a triple D to a D or full C.  The circumference (40) remains the same.  Any less and your breast shape will look a little flat.  Your base is just too large to have a good-looking B-cup.  But a C-cup is very doable and will make a huge difference, and alleviate your pain.  I've attached a link.  Be sure to have a vertical reduction, not an inverted-T "anchor" reduction which is causes more scarring and a less flattering shape.  I've attached a link in case you wish to see some examples and read more.  I know your symptoms are your priority, but you can still look good and change your breasts from a negative to a positive in your life.

The patient can pretty much determine any size as the result of a breast reduction. Major reductions may alter the technique. This will be discussed with your plastic surgeon.

It is possible to have a breast reduction to a much small size but you must be able to keep tissue to ensure healthy healing. Cup size is irrelevant to me and I reduce the breast significantly but to match your chest/hips. 

Dr. ES

can vary considerably with how aggressive you wish to be with removing tissue.  But you must be cautious in what you desire because if you experience any weight loss in the future, your breasts will shrink as well and you will be 'out of proportion' but if that doesn't matter to you, you could easily have a much smaller size.  Cup size cannot be guaranteed.

Thank you for the question.
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.  
The other concern with overly aggressive breast reduction surgery is patient dissatisfaction  afterwards.  It is not unusual for patients who have lived with very large breasts to want to have as much as possible removed. Care must be taken to be judicious in this removal to avoid an outcome where the breasts  are too small in relation (proportionately) to the patient's other body parts.  Again, it is not uncommon, for patients'  breasts to become smaller ( after the breast reduction procedure) with time and/or weight loss-  breast augmentation may become necessary to achieve the patient size goals.
 Most patients  undergoing breast reduction surgery wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso. 
With the goal of improving communication with my patients (determining their goals in regards to breast size after breast reduction surgery) I find the use of photographs of “goal” pictures (and breasts that are too big or too small)  very helpful. I have found that the use of words such as “natural” or “B cup” etc. means different things to different people and therefore prove unhelpful. 
Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup  size may also be inaccurate.
 I hope this, and attach link, helps.