I absolutely think so...I think that sometimes the question is: how secure a gay woman do you have to be in your relationship with a bisexual woman...sometimes gay women spend so much time terrified that the bisexual woman they are with will inevitably go 'running off with/back to men' that they damage their own relationships internally. People cheat sometimes, period- be it with a man or a woman. Trust is rough.
So I guess one should consider their own state of security before getting involved with a woman who adheres to a bisexual label??? my take.
Bisexual women are more than capable of being in a committed relationship. As Jannelle stated, it's a question of one's own insecurity. It's important to understand that bisexuality has little to do with the genitalia of one's partner, but rather deals with the connection one has with another individual.
I think that being bisexual has little to do with how involved a person is in a relationship. No matter if a person is gay, straight, or bisexual if they are not willing to fully commit to the person of whom they're with, then cheating may be a possibility. I'm not saying that its right but you can't judge all bisexual women and say that they have a harder time committing to their partner then gay women.
As a bisexual woman, I can tell you that the ability to commit is a personal trait - not something defined by sexual identity. What's more important is the ability to communicate and be honest with your partner(s). One problem I've found is that people don't take bisexual women seriously. I easily get dismissed as the "straight girl", and I miss out on many opportunities with women who are too insecure to get involved because of the stereotype that bisexual women can't commit.