The engine compartment gets water spray from the tires and through the radiator all the time... Nothing to worry about... Go to Home Depot, Lowes, WallyWorld, or a garden store and buy a generic water hose garden sprayer. Put a generous squirt of Dawn dish soap in it, hook up the hose, and soak down the engine compartment. Let it sit for a few minutes and hose it down again. Rinse and repeat a few times...
I don't bag or cover anything, I just avoid a direct shot of water into the alternator, air intake and fuse box. I'll also usually give the batteries a good cleaning with baking soda if they look funky.
That's all I've ever done to get the mud, blood, and crud out from under the hood... I've never had a problem.