Revisiting the episode, the HIV conclusion was based on the fact that they thought the mononucleosis was presenting in an unusual way, consistant with someone who might be immunosuppressed. Since the most common way for a sexualy active person to be immunosuppressed is to have HIV.
They also used the HIV test on his fiancee as a threat for the patient to come clean about his previous relationship.
As to the gay/straight thing, I think more of the dialogue was used to target the fact that he tried to cure himself of "the gay". Wasn't one of his symptoms Erectile Dysfunction, specifically while he was with his fiancee?
I don't think the ability to label him bisexual was possible, because he wasn't operating with equal behavior towards both sexes (again, the ED), at least as far as the show was written. As for whether or not the show was well-written, I don't know. I've never been pulled out of a House episode because something was written funny.
Plus Thirteen has that whole chip on her shoulder about being honest with one's self. I don't think she's bisexual so much as indescriminate about her sexual partners, which is fueled by her assumed shortened life-span due to the Huntington's disease. However, the whole relationship with Foreman is the typical human desire to connect and to experience deeper levels of relating with another person.
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