I had a short fling with my english professor when I was 18. But she wrote her number on my term paper. She used plausible deniability (an excuse to be alone that doesn't mention sex). She wanted me to teach her something. I forgot what it was. In fact, every girl that number closed me that year used plausible deniability. It's female game. If she wanted to be alone with you she would have already given you an excuse, in my experience.
I've never been in a situation where there was clear interest and the woman didn't throw me a pretense to be alone with her so that I could jump through her window and escalate. When women like me, they actually help me out. A LOT. I don't have to be a mind reader and figure everything out by myself or go to some online forum and ask random strangers for advice. The way I look at it, if she really wanted it, it would have been clear. Anything short of clear interest is validation. Seduction isn't something you do to a mannequin. She has a mind of her own.
I am not saying I have never tried to escalate without clear intentions from the woman's part. I have. And it's always led to awkward moments and rejection. In her mind it's like "Okay where did that come from? I never gave you a clear sign. Flirting and attention means nothing." There was never a time in my life where I was able to summon some magical game to seduce women if they weren't already trying to seduce me.
Guy's underestimate women's need for validation. They are shameless in that department. Until she gives you an excuse to be alone with her where something can escalate, you really have nothing. Well, you do have something. Your role is to serve her and validate her. You are a tool in her ego validation ecosystem.
this is definitely not an absolute. i worked with a girl at a trading job and she deliberately picked her desk to be on the opposite side of the room from mine because she didn't want to be distracted by me(she confessed this to me after many months of seeing each other). people would always go take lunches together so one day i went with her and some coworkers. the next day i asked her if she wanted to take a walk, she was receptive and agreed. easy banter and jokes, then when we were chilling at a park on the water i looked at the view and said 'you know i really want to kiss you but i don't want to get fired'. she immediately latched onto me and shoved her tongue in my mouth, we fell and were rolling around the grass like a couple horny teens with our tongues deep in each other's throats. every day after that we would leave for lunch together, sneak into a locker room of a university a few buildings down where she used to study, and fuuck like rabbits. that locker room floor is covered with my gentleman relish.
anyway point is she showed zero signs from the start and even deliberately sat away from me so she could focus on her work. even when she was receptive to my invite it was in a friendly way, i saw no real signs aside from her being a little more excited than i expected, and i took a massive risk by saying what i did by the water. it paid off and i think if you get good at really feeling women out the chances are 50/50 or higher. if a girl rejects in such a situation i say "ah well... that's the only chance you're gonna get. i hate to do this but i'm putting you in the friend zone, it's for your own good." just something stupid and funny like that to avoid awkwardness, then forget about her.
OP this is a high risk situation. from what you've described she's just being a friendly teacher and she could easily get your ass kicked out if you do something stupid. i would polarize this women asap to avoid any mistakes or wasted time. don't ask for something lame like a lunch. ask her for something more personal where the answer will tell you her intentions right away. tell her about a good bar by your place and ask her if she wants to grab a drink to unwind. pick an evening time so she has time to go get dolled up. her response will immediately tell you if she's only been a friendly teacher or if she has any real sexual interest in you. if she declines without a counteroffer then forget about it. if her counteroffer is something friendly like a coffee or lunch then she's just being a friendly teacher. if she accepts without resistance then you're pretty much in. meet up at the bar, banter, play some pool or something stupid, make some stupid joke or excuse to test touch, gauge her response, if it's positive again you can pretty much say anything and go in for the kiss.
if this sounds daunting then don't do any of it. this requires hot guy smoothness and confidence. you have to know you're the shiit and act like it, but in a humble sexy seductive way.