This advice is too late for the OP, but in the future look at buying a mower with an aluminum deck. I have had mine since 1994 with no rust issues and only a couple mechanical issues with the B & S engine.
Change your oil. Take an old paint brush and slather the under side of the deck. Don't worry about attracting dust and dirt. That will HOLD the oil TO the deck which prevents corrosion. Great way to recycle your used oil. Do the same thing in the fall when you winterize the mower. Slather that deck up.
