I would say that this is a bit of a red flag. Even if she wasn't openly bisexual, the picture of the male ex there is an alert. If she doesn't want any "relationship exposure", she should have taken the picture of the ex down. Now, this could also take on a different meaning, and that is, she's serious about women, but just isn't as into you as much as you are in love with her, which is not a good sign either. But you know what? If you aren't exactly thinking of genuinely marrying her at this point, perhaps you can just enjoy the love that both of you have, and look at the bright side. Perhaps it's a misunderstanding and it will turn out alright.

This is a bit off-tangent, but when it comes to bisexual women, I've got several inklings as to how much (or not) they can be into women over the longer-term. It's very important to note that sexual orientation awareness doesn't always fully cut it. There are bisexual women with a common sense view of sexual orientation or a romantic view of women, but they will not necessarily stay in a lesbian relationship. So, these are my thoughts about this matter, if you will.

1. Society success/tradition -Aside from money, the next thing human beings crave quite a bit is societal success. And one of the most easily attainable, at least on a technical level is heterosexual marriage. The whole settled house, marriage, kids, along with mainstream approval/praise and full societal support. It's why a lot of bisexual women and men end up with opposite sex partners. Gay marriage does not apply. You are still outside society no matter how great your partner is. Then there is the fact that some women do want kids and to raise them as a family with their spouse. So, if a bisexual women banks a lot on such society success, it's more likely that she won't stick around in a lesbian relationship.

2. Relationships with women -More serious bisexual women have actual thoughts about being with a woman. Not just surface-level stuff, like "being attracted to a woman is no different to a man" etc.. Just like lesbians think about what type of women they love, the kind of partner they wish to have, what kind of life they desire if they are in a long-term relationship. Genuine bisexual women who are interested in women over the longer haul, usually will have deeper in-depth thoughts about women. Like, there should be more details on what she can say, and not just platitudes or statements.

3. The bisexual umbrella -Bisexuality is a rather large umbrella. It consists of women who are more attracted to men, middle-of-the-line-bisexuals, women who are more attracted to women. Naturally, women who are more attracted to women will be more likely to stick around. Middle-of-the-line-bisexuals are trickier, hence points 1 and 2 to check her out. Lately in this climate, I think some sexually adventurous straight women are calling themselves bisexual while some other types of bisexuals are calling themselves queer or lesbian.