I have a naturally occurring “double bubble” in my breasts. Is this common?

Thank you for the question.  It is an important one: selection of your plastic surgeon will be the most important decision you make when it comes to achieving an outcome that you will be pleased with.Definitive advice would require much more information. I suggest that you submit photographs, side and frontal views, taken by a second party with your arms by your side.
 
Generally I suggest that patients start with the American Society of Plastic Surgery and/or the Aesthetic Society of Plastic Surgery to obtain a list of well experienced board-certified plastic surgeons.
Then, I would suggest you visit a few surgeons whose practices concentrate on aesthetic surgery. 
***Ask to see lots of examples of their work and preferably speak/see patients who have had similar procedures done.  Reading online reviews can be helpful in this regard also. Ultimately it will be important that you feel comfortable that your plastic surgeon have a significant/demonstrable experience consistently achieving the types of outcomes you will be pleased with.   
Besides appropriate training and experience (and certification by the American Board of plastic surgery), looking at before/after photographs (and preferably talking to previous patients) can be very helpful in this selection process. 
 Basically, patients should look at the overall "quality"  (as well as quantity) 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".
 
I hope this helps. Best wishes.

Without photos and/or in person examination, it may be difficult to answer your question. You may have a form of narrow base breasts or even tuberous breasts that will definitely need examination before surgery. You should schedule consultation with a board certified plastic surgeon with good reputation in breast surgery to discuss your goals and options. Good luck.