You and Alex are getting along great for this stage of your relationship. Greys are very slow to trust. There was lots of good advice given. As Accapella said, don't let your hand come at him from the back, it will freak him out every time. Also, unless you were dripping blood and had hanging skin, that was a warning, not a true bite. I say this from experience and have the scars to prove it. Give Alex more time. As some one else pointed out, he lowered his head a few times. When Timber does that he wants a head rub. Be careful though, he could still startle and nail you. Take at his pace, which is probably sloooow, and try some of the things mentioned.
This may not apply to Alex, but I'm going to throw it out there. Every time I would try to get Timber to step up on my hand he would bite. I also can't say "step-up." Not sure what happened in his past, but those are no-nos. I finally found out he will step up on my forearm, and I use "wanna go?" as the command. One of the hardest things about rehoming is not knowing their past and what makes them react like they do. It's a learn as you go thing.