There are two issues here, it seems to me:
1) That you feel confused by what your T said/did last week and it made you feel that maybe she would be willing to be friends with you. One way you could tippy toe into this conversation would be to raise your confusion.
2) I just think you explained really well what you were looking for from her, in a very nondemanding, mature way. However, I really wonder about the timing of saying this NOW (particularly since you also have a trauma agenda for this session as well, as you said in another thread). Have you thought about how it might derail your therapy if she answers in a way that is other than "yes"? And why you want to raise this issue now, as opposed to near the end of therapy? What are you hoping that her answer to this question will do for you?
No requirement to answer these questions. I get the urge to ask. My T offered to walk me out to my car after last week's session because a somewhat aggressive panhandler has been coming up to me after I get into my car, asking me to roll my window down. I felt a stab of regret as I left him at the curb, a kind of regret about not having met him under normal social circumstances. I think he would be a kick @ss friend. I've had men friends all my life, but I currently could use one right about now.
So I've been thinking about this issue these past few days, but I know that if he were to say no, or to defer the issue until I'm ready to quit, I'd be really hurt. Even if the answer were what I think the rules are for his field -- social relationships only after 2 years post therapy-- I'd still be hurt no matter how much I would intellectually understand that he couldn't. What, you won't break the rules for me

?
Anne