without all that eye goop porn stars usually wear.  I was trying to figure out a dicreet way to ask if she provided, but the best I could think of was: "Have you ever heard of TER?"

I chickened out and didn't ask her even though I had a good opportunity.  How would you handle a situation like this?

First step, have the conversation where no one else can eavesdrop!
Second, your job is to approach her identity first, asking about providing too early makes you look creepy, and she will deny it.
Say something like "You look so familiar to me, are you maybe an actress? Is your name Tasha?" If she says "Yes, that's me," then you go on and mention you are a fan of her work, enjoy her movies, etc. No mention of details, favorite scenes, etc. Keep that on the low. Don't ask her for an autograph, as that will bring attention to her, with other guys asking her "Who are you? Why are you famous?"
If at this point she is having a conversation with you, now you can broach the subject, but again a direct "Do you provide" won't work. You have to be a little more subtle - "After we land, will you be working? I would love to see you and spend some time with you."

If she seems like the spacey type that might be into Karma and Astrology and shit, throw in "I don't want to miss out on this, as it could not have been an accident that I am on this plane with you, and was able to recognize you."

Whatever you do don't lead with do you provide. Even if she does she will say no because you wii come across as a random creep. Be chill and say something normal. Your instinct was good, just need to trust it.