She's so obviously not actually straight.
What's interesting is that she never once claimed to be, either. That's all an assumption on Hana's part.
All we know at this point is that she is afraid of acknowledging Hana's feelings, because she never has had any relationship of any kind as stable as this one with anyone else before, man or woman, and she does not want to destroy that.
What we don't know is if she thinks that it would destroy their relationship because she is straight (increasingly unlikely, as you rightfully pointed out) or because she simply sucks at having stable romantic relationships.