You need to make sure it is not leaking from the cooling system while it is sitting still in the water running. If the drive shaft is leaking this should also happen when sitting still or idling (just maybe not as much as it does moving faster).
If it is the drive seal, I would try just adding more marine grease through the grease point with a grease gun first. If that doesn't stop it, then you are probably looking at replacement and $$$. Good luck.