I think the kind of therapist most likely to do 2x week is the kind of therapist that has openings in his schedule.

I have never scheduled 2x week, but have had "emergency" sessions on occasion, maybe 6 times in the last year or so. Very infrequently over the course of the last decade. It does help to deal with the intensity of what comes to the surface and it sounds like you are not fooling around, you just want to drop into it.

As to bonding, I tend to think it's a natural product of feeling heard and seen in therapy. I think you are just talking about bonding, right, a kind of connected feeling and not the intense attachment/love pangs that are sometimes discussed on this board? I think that is individual in nature and I'd be surprised if that was what was sparked in you, given your goals going in. And I don't think that has anything to do with 2 or 2 x week.