Lyric discussion by breakdowngasm 

Cover art for Bridle lyrics by Sage Francis

I think the reins/bridle thing is about the marriage, which is kind of what broccoliandcheese was saying, it's control. Before a woman is married, she's "free", and when she's married she's not, because it's her job "as a woman" to look after him and make sure his needs are met.

He but the bridle on her, took control of he, made her his, like a horse. Marriage.

But, I think she cheated on him, the entire song sounds like he's chasing her.

"He’s dumped, and can’t seem to swallow these lumps The beat goes on…"