He clearly has ability and he's shown it in glimpses but he seems to have major problems with confidence. At times, he looks scared, shies away from the ball and doesn't take responsibility as a creative player.
Maybe it's because he's playing in a League that is far better than the one he's used to or maybe it's just the style of the League, the quick tempo and the fast paced games. I couldn't say, probably a combination of both.
Positionally I'm not convinced his best position is wide left either. I look at someone like Niko Kranjar and that's the type of player I want to see Bilyaletdinov develop into. Not the quickest but tons of technical ability, trickery and intelligence. But the majority of these players are central players who play outwide, usually on the opposite wing to there natural foot: Left footers on the right, right footers on the left. They can cut inside and influence the game in central positions.
As a left footer playing on the left wing, it's completely different. Because of your body positioning, the only way you can really go is down the line and that means beating opposition players. Something Bilyaletdinov seems to have trouble with.
In short, I think he'll be a good player here but I hope Moyes gives him freedom and tries him in different roles so that he can fulfill his talent and find a role in the team.