there isn't much use scrubbing the engine bay because you can't access all the nooks and crannies of it, so better get an all purpose cleaner, 3M or some other good brand, spray the bay with water, spray APC on it, use a cloth/brush and scrub the areas which are easily accessible, give it a minute or two, rinse all of it and blow dry it. give the plastic bits a good dress afterwards. you're good to go. this way, the unreachable areas would be cleaned to an extent by the APC.
For water, use high pressure water, if you don't have access to one, you can go to the service station then.
using the garden hose for engine bay is pretty much useless
For reference, the attached pic is of my civic's bay, Procedure was as follows
Rinse with a pressure wash, 3M apc 1:10 dilution sprayed, rinsed again, air blower dried, meguiars engine dressed used on the plastic bits. this cleaning lasts you quite a while depending on the usage.