I had the same problem as yourself last year. I went to my local fabric store (JoAnn's) and in the notions section they sell pre made bra cups that are made for swimming and/or gowns. I had my local tailor sew the cups to the lining in the bra area. It worked perfectly with nothing showing on the right side of the fabric. I think this would work for you very well.
Samll Busted - Adding Bra to Swimsuit
in Cruise Fashions & Beauty
Posted
I had the same problem as yourself last year. I went to my local fabric store (JoAnn's) and in the notions section they sell pre made bra cups that are made for swimming and/or gowns. I had my local tailor sew the cups to the lining in the bra area. It worked perfectly with nothing showing on the right side of the fabric. I think this would work for you very well.