So I'm going to try to befriend my speech therapist, she seems interested in me, she touches her hair, her pupils dilate when she looks at me, and she's very responsive to whatever I say. We get along great and she's easy to talk to. I've been in a lot of situations where I'm somebodies client/student/patient where I feel like this person sucks. This is the one of the few times where I feel like this person is awesome and want to be friends with them or something more. She's a 7/10.

I only have two sessions left with her and I was wondering when the best time to say this line is "Since we won't be meeting anymore, we should keep in touch and possibly do stuff together." I was thinking either before the session begins or after, maybe even during. The therapy rooms have cameras in them that record audio, not just video. They review each session with their instructor, so if I say the line during the session the instructor will see it. The therapist here are actually graduate students. My speech therapist is not going to be their next semester, I was thinking why not give this a shot. So I may say it during the second to last session. I've talked to a lot of people about this, they all say go for it. What do you guys think?

If you don't go for it, you'll keep living your whole life wondering what would've she said if you did do it.

So just go for it.

She's not interested? You move on.
She's interested? You get her.

Both ways you're better off going for it.

Go for it. You have nothing to lose, and if you don't do it you will end up thinking what would have happened if you had made a move.

As for time, I'd say do it on the next session (preferably at start), if she says nothing, wait, and don't look desperate. She may think it over and give you the O.K. If she says nothing during the last session, bring her a gift (some flowers, or something) to thank her for her dedication and hard work, say it was a pleasure and give her your business card saying something like "call me if you want to meet for a cup of coffee or if there is anything I can do for you".

And do it away from the camera. She may say no just to look professional.

Yep, GO FOR IT. You don't want to live the rest of your life in regret. You got this. Either way (yes or no) you will feel good about yourself for having taken the shot.

So I said the line before the 2nd to last session, she said "OK, we can figure something out. I don't know the catchcall on that though." We did the session as usual, near the end of the session. We went to the copy machines to copy material I can practice with till our last session, while walking she asked me about my B-Day and what kind of cake I had. I said a chocolate cake from Cosco, we started talking about how awesome Cosco is.

She ran in another "client", I introduced myself to him found out he isn't a client he's actually a professor. As we continued on with conversation she said from the other side of the room while smiling "He's my teacher." Anyways she finished copying my material and handed it to me, and I left the building.

What she said initially means nothing I say that all the time to people I do and don't want to keep in touch with. I've done this before with one of my teachers, I remember after messaging each other a bunch and finally securing a platonic breakfast date. I in my car inside the parking lot, thinking of the possiblilty of her not showing up. In wich she did show up, and we've been hiking together ever since.

So we'll see how this turns out.

GO for it! you dont want to be regreting it the rest of your life

I forgot to mention I acquired her number when we first met. What does she mean by "I don't know the catch-call on that though."?

I've been talking to people about this, and they say keep going for it. One of them says to text her. The only time I texted her was when I had to change the appointment due to work. Do you guys think I should text with her, and what should I text, or should I hold off on contacting her till the last session?

Don't text her. That comes off as lame. I've never had success with it.

At the last session just say something with a bit more edge. Be short and to the point; I'm sure she understands how dates work.

Say:
"I'm going out for drinks tomorrow. Come."

If she says yes, NICE! If she says no then don't say anything. Remain calm. She'll probably give you another day or will give you a bunch of bullshit reasons why she can't. Then wait a couple days and text her something funny and relevant to your discussion of a date. For example, if she gave you some silly excuse about you being too young, text her something like...
"We're both a few days older and a few days more mature now "

Or she said that it was unprofessional to date a patient, text her saying...
"I'm not your patient anymore "

_________________
The ultimate lesson of psychoanalysis is that human life is never "just life": we are possessed by the strange drive to enjoy life in excess, attached to a surplus which derails the ordinary run of things.
-Slavoj Zizek

There comes a time when living inside your head is too much of a hinderence! Just go for it mate! Most importantly, learn from it!

You should call yourself the Cunning Linguist around her...

Sounds like you're both being a bit cryptic. She with the "catchall" part, and you fumbling about saying the two of you should do "stuff" together. She may be wrestling with the question as to how you see her.

You can save yourself a lot of time and potential drama but simply declaring what it is you want out of this. I would shoot her a text, or better yet in person.

She's a therapist of sorts, I am a therapist. I can tell you there are ethnical codes that even a graduate student must abide by to protect themselves. Since this is strictly linguistics, I don't think there would be any hard and fast rule about dating clients, but it was a good call to not do this in front of her peers just to be safe.

There is a power differential in the relationship as she's the teacher, and you're the tort. Which at some level you can tease into fantasy play, but that's much later in the game. Right now I would keep the reminders of your sessions with her to a minimum this may create a bit of an ethical dilemma for her.

I'd invite her out somewhere public, maybe for lunch

All right I think I blew it. I was feeling very sick during the session, I felt like I was going to puke on myself, and I was sweating too. When I feel sick I don't think straight at all. Anyways here our the mistakes I did. I said this during the session "We should got out and have lunch sometime." She said "I have to ask my supervisor if I can, all because of professionalism concerns." That was mistake number one, I was supposed to do this before or after the session, not during.

So hours after the session I was still feeling sick, she texted me this "Hello. Sorry, I won't be able to have lunch. It was nice meeting you, good luck next semester!" I texted back "Thanks for letting know about lunch, I understand that you want this to be strictly professional." I should've said "Thanks for letting me know, is their anyway we can keep in touch?" So my sick self blew it, I hate being sick because I do so many things that otherwise I'd never do.

Anyways I'm feeling a little better today.