What does it mean when someone says 'I'll be your bitch'?

One slang meaning of this Word is to be subservient, a servant. He's saying he'll bow down to you and do what you want.

I'm a dude, and I say it all the time to my mates when pratting around, such as 'dude I'm gonna totally make you my bitch' or 'you're my bitch'. This isn't said in a homosexual way, it's just a friendly thing. But yes, if a bloke is a screaming bender, he may quite possibly refer to his partner as his bitch.