Tourists in Rome sometimes forget that the Eternal City has a lot of beaches around. You can make a great beachwear shopping and easily go to Ostia (where you can get there by subway from Piramide), Fregene and Maccarese. The region of Lazio offers also other places such as Sabaudia, Circeo and the wonderful island of Ponza.
There are different brands in the city to get bathing suits. For men in Cenci and Battistoni for example. For women if you don't want to spend too much, Calzedonia can be a good choice. In the picture below, one model of the new collection. Different shapes for bikinis and long bathing suits. Colours can range from a feminine pink to blue, white and red in a marine style. The Calzedonia stores are spread in the city especially in via del Corso, via dei Giubbonari and via Frattina. There are other easy brands that you can check like Tezenis and Intimissimi in via del Corso.
If you are looking for an artisanal bathing suit, something really special and unique you can also go to Marisa Padovan in via delle Carrozze 81. We can call them Beach Couture. She made also nice sundresses for lunch on the swimming pool. Also her daughter Flavia designed her own collection She made a nice video on youtube.