Punch to the rescue:

This rather charming cartoon from the 3 August 1867 edition of Punch (see http://www.victorianweb.org/periodicals/punch/seaside/15.html for attribution etc) clearly shows that most of the young women depicted are wearing a simple shift.

Which makes perfect sense – it allows reasonable freedom of movement, hides the shape of their bodies, and probably allowed them to swim a few strokes if they wished.

Given that photography in the 1860’s was a cumbersome business there are very few beachside photographs, however Punch cartoons, satirizing as they do the habits and foibles middle classes are drawn from life and are mostly reasonably accurate as regards dress, etc