From one of Banner's lines in The Avengers
(when he touches the cradle while talking to Natasha), I'm under the impression that he's deliberately keeping his distance. He may have more control over his situation, but he's still obviously not leading a normal life. He probably thinks that she doesn't need the "always angry" Banner in her life...and it's not clear whether or not he could safely consummate his relationship with her these days. If he could, it would presumably be...angry.
Plus, the same scene implied that General Ross was still interested in finding Banner, but SHIELD was doing their part to throw him off track. Ross would still be keeping a close watch on Betty for any signs of Banner contacting her.