Is my Girlfriend being paranoid or am I being naive? ?

Ok, me and my girl go to the same college. She is in a different program than me, so we have different instructors and different days that we go to class. Well one of her instructors has a HUGE crush on me (he did even before her and I started dating). He says he wants to check out my Myspace page to see my pics, he tells me that older men "do it" better (in front of my girl) and he invited me to in new house for dinner.

Its starting to cause tension whenever she goes to his class. I just smile and brush it off, but my girl seems to think that I flirt and cater to his gestures because I don't out front tell him NO. But for awhile we were trying to keep our relationship low key at school, but we've been getting closer and more people are starting to piece things together about us.

I don't want her to snap on her teacher because of me, but I don't feel I'm doing anything wrong by taking the passive road hoping this professor will get the picture. NOTE: I think he equally plays naive, because I don't think he knows I'm bisexual or that I'm dating my girl-I think he thinks we're study buddies.

Is she being paranoid, because Im bi(she has expressed concerns about me not being fully gay) or am I being too passive in dealing with this man?