What I do is vacuum the element with a shop vac pulling the air back in the opposite direction that the engine does. I then saturate the fiber mesh with Simply Green. Let that sit for about 10 minutes and then do it again. After that sits for 10-20 minutes, I then submerge the entire element in soapy water (dish soap) and "swish" it around to get the dirt out of the element. Then I rinse it with the sink sprayer washing in the opposite direction to the air flow. Let it dry in the sun and slap it back on the bike.
I do advise that you wait until the missus is out shopping so that the unapproved use of the sink will go unnoticed!!
TQ