Hey man, having a bisexual partner has its benefits...
Joking aside, I would have absolutely no problem with it. Why would I? Sure, it opens up another potential avenue for her cheating on me, but if I'm constantly worried that she could be cheating on me with another man or woman, then we aren't going to have a very healthy relationship. I guess, for some people, it could cause some self-esteem issues, as you know you're only satisfying one side of their sexual desires, but in any relationship you likely aren't the only person they're attracted to, regardless of sexual orientation. A heterosexual partner will likely be attracted to other people of your gender. Opening it up to more options should not make things any worse.