If you're going to go surfing, you need a special bikini, not a regular bikini. Bikinis for surfing are designed out of special materials (often neoprene or rubber and a mixture of other materials). They fit the body better as well. A regular bikni mighty not stay on in the waves.
Here is a very cool neoprene bikini from Ebuddy. It comes in lots of different color choices. It's not too sexy, so you won't feel like your shooting a sexy calendar when your out on the waves. The bottom is tight and snug, but not cheeky like a Brazilian or Thong, so you're not exposing too much skin.
Here's another nice surfing bikini. It's made with Polyamide and Elastane. The bottoms are a bit cheeky, but if you prefer a more modest bottom, you can choose from several other designs. There is also an even cheekier one, almost thong but not quite, that's awesome. It's a very cool design, is perfect for surffing, and comes in a variety of cuts. The photos below link to the bikini bottoms, but you can also find the tops sold on Amazon--usually on the same page.