The onsens are a little bit different from that ... at least the one that we went to. There is the shower/bathing area, and then a series of warm-to-hot pools in which you can sit or swim a little bit, although they are fairly small. You move from one pool to the next, with perhaps a bit of a "dip" in a cool water area in between.
The only thing you have with you is a small washcloth, which you use to sort of cover yourself when you go from one pool to the next, and which you fold and place on your head when you're in the pool. No bathing suits of any sort.