To answer the original question - not many.

Steve Gibbons Dylan Project (with members of Fairport) has already been mentioned. Steve and Fairport have always done Dylan songs, so this was a logical extension. Never seen or heard of Dylanesque, but know of their existence.
I have long been friends with Bob Phillips from Warwick, who has always done Dylan songs, and he put a band together which is very reminiscent of the Band period. I think Bob P knows every single Dylan song, and going to see his band is a pretty fair sustitute for the real thing (better sometimes given Dylan's somewhat variable output in recent years). But Bob P is very sensitive about NOT being labelled as a tribute band and all it's naff connotations.
He was increibly embarrassed when some friends in the pub put him forward for Stars in their Eyes (or one of those progs). The good sport that he is, he went along with it, but was horrified when they made him wear a Bob Dylan wig!! I think he came third.
We recorded a CD live on Bob Dylan's 60th birthday, and at that time did some research to see how many other tribute bands there were. As I said at the beginning, hardly any.
We even tried to get him signed up with one of the Tribute Band Agencies, but there were no takers. Perhaps Dylan doesn't have the same popular appeal as Queen/Abba/Beatles/Stones etc, of which there are hundreds.
Or maybe Dylan's music, the people that play it and those that like it, do not fit into the normal entertainment world.
Obviously a good thing.

Graham