Coming from kayaking, I'm used to having stuff on me while paddling - extra water (a must have), an energy bar, maybe a camera, and extra clothes in case the weather turns. This became a problem when I started to rent sups a year ago. I compensated by finding a cheap fanny pack that I could cut holes in the bottom of the pockets to allow water to drain. When winter hit, the fanny pack wasn't big enough for an extra paddling jacket or what have ya. So I attached bungis on my board using NSI attachment loops to strap a dry bag down. This has worked great for smaller stuff.
Other options include using deck bags designed for kayaks. The above bag is made by Sealline (owned by Cascade Designs) in Seattle that makes waterproof bags of various types. These bags have waterproof zippers, bungis, and other options to strap gear down. The bags snap with buckles to your board via your bungis or whatever system you have figured out.
The only downside to bags on your board is the extra weight on the nose that effects carrying the board on land. Even an extra water bottle throws off the balance of my board. Most are putting gear on the nose.
Find this product at Northwest Outdoor Center in Seattle.