Bromance is a very close relationship shared between 2 males.
It is where both of them are comfortable in sharing their thoughts, feelings, secrets, etc. with each other. That person is your confidant and you genuinely care for him.
Typically, the relationship is between 2 heterosexual males.
I am not saying that gays are usually left out from having a bromance. It can happen. However, in cases where a bromance is between a gay person and a heterosexual person, it is difficult if feelings are involved. As the parties in the bromance are very close, feelings for the heterosexual person could start to develop. Therefore since these feelings are not reciprocated back, it is difficult to maintain this bromance. The only way a bromance can be possible is if both understand that the bromance will not proceed further into a more serious relationship (unless the feelings for each other is mutual).