Invest in some basics such as a T - shirt bra for your regular T - shirts / tops, a lacy push up bra for those parties and night - outs and seamless panties to hide visible lines under your denims and dresses.
Typically, I massively dislike visible petticoats peaking out from under vintage style dresses, but with this dress I think a touch of black chiffon or tulle visible against the sheer floral border looks beautiful.