I hope you guys don't mind if I chip in a little bit! I have had a curious relationship with the bromance as I've transitioned from male to female, and paradoxically, being able to transition to a female has allowed me *greater* camaraderie with guys.
Part of it had to do with identifying as a gay male beforehand, which, I felt, isolated me from males (and didn't allow me much interaction with females beyond "hey, let's coo over a hot guy". As I began to transition, there was a weird liminal period, but eventually, my sexuality shifted towards attraction to females.
This, it turned out, was the key. Being just divorced enough from malehood (as a passable, pretty female) while having close to zero sexual interest in them basically prompted my initiation into brohood with a few of the guys I know. And, from my interpretation of the word bromance, this is pretty much as close as it gets.