OK this happened to me on my WR250F last weekend so I have been doing the research on it:
1. Remove air filter and squeeze out all the water you can - leave it off. Empty all water/mud from airbox.
2. Open the drain bolt (17mm) on the bottom of the carb - let fuel/water/mud run out, let some tank gas run out too. Replace drain bolt.
3. w/ bike upsidedown remove sparkplug and pump the kickstarter with your hand. Keep eyes away from engine as water n'stuff will come out of the sparkplug hole.
4. Replace spark plug with new & dry one. Kick until bike starts.
5. Replace air filter, tank, shrouds and seat - then ride it home.
... sounds better than what I did to get it started LOL.
I did this to my XR last year. Clean the airbox thoroughly. Drop the float bowl of the bottom of the carb and clear out any sediment. Stand the bike on the back end and drain out the pipe. Change the gear oil. Then warm the engine to full temp and change the gear oil out one more time to get the remaining water out if there is any. I can't think of anything else except maybe actually cleaning the carb itself.
One other important note - Check your oil when you get back to the truck. If it looks at all milky or white, change it immediately. I'll do an extra couple of miles just to work it through then check the oil again.
A friend sunk his WR400 and left the watered down oil in there for a month. I'm sure it started rusting all sorts of things.