I think that Bruce talking to Cass about the matter was such a natural progression for their relationship at that point. As for why he chose Cass to talk to this about, as I mentioned, I think it's because they're are so alike in being broken. What happened to Bruce as a child was extremely traumatazing and set him on a path from which it was too late to deviate when it even became a possibility. He can't be anything else than Batman, there's nothing else to him but to try to stop what happened to him from happening again. There is no possibility for a happy ending, for a great love or anything of the sort, it's too late for him and he realizes that.
Dick on the other hand had managed to grow in to an extremely well-adjusted young man, who had made his own legacy, but at the same time did what he did because he wanted to, not because there wasn't anything else he could do. Tim had surviving family, at that point at least, and it actually looked like he could give up on being Robin at some point. There was no unhealthy obsession in him, no force driving him as great as with Bruce. And Babs? She was another tragedy, another casualty in Bruce's war and another thing he blamed himself of.
Cass instead was someone who was also broken as a child and from whom that possibility of a normal life had been taken from. She, of the choices, was the one who could understand what it means for people like them to have that choice of living a normal life, how in the end it is what they desire other people to have. It's almost a shame, as I again read this, because I do honestly think they might have put more focus on the relationship between Bruce and Cass in the main titles if they hadn't been forced to do an emergency juryrigging of the Steph-as-Robin storyline.