Soldato
You shouldn't need to wash after claying. Get straight onto the polishing stage.
Shouldn't need is somewhat true, but I still think it's a must. You've spent that long so far, what's an extra 10-20 minutes harm in giving it a quick wash? The clay bar sometimes won't "pick" up the dirt but simply aggravate it, and with the lube/water just move it to another area. You could just use a plush microfibre towel to pick up such loose dirt. But I prefer a good blast with the jet and more suds.
Just my 2 pence...