The couple have kept their relationship under wraps since meeting through mutual friend Jennifer Aniston last year.
A source told Star: "A few weeks ago things got a little more intimate between them. They are really bonding - they have more in common than anyone thought."
Bing filed a lawsuit against Hurley to establish whether he was the father of Damien, now five. A DNA test subsequently proved that the baby was his.
Crow split with Tour de France champion Lance Armstrong in 2006.
She recently claimed that Aniston had dumped husband Brad Pitt rather than the other way around.