Do you have to bring your own swimsuit?

For floating, you're in a private tank in a private room, so you're naked. For the sauna, again, private room, private sauna, naked (if you go from the sauna to floating you're provided a robe). Not sure about massages but usually you just wear underwear or a towel.

Simura is correct. In fact, it is highly recommended that you don't wear a swimsuit while floating because it can cause extra sensations, which is what you're trying to avoid.