If your ignition is wet, the output of it may be reduced. This may still show good spark with the plug grounded on the cylinder head, but when under compression in the engine, the spark may be too weak to jump the plug gap, hence it won't fire under the compression. Drying the ignition parts out, may let it build a stronger spark again, and it fires under the engine's compression again.
Unless you have fouled a spark plug trying to start it, or physically damaged something with the pressure from the water, it is unlikely it will cost you anything to dry the bike out and get it running.