This is a relatively unusual situation. Your young lady has passed the age of invincibility where kids will try things with less fear of consequences.
Q1 Does she have hearing issues or balance issues? If yes, then there may be a medical cause. If she can walk and run fine, then she can ride a bike.
Q2 What kind of bike was she riding a decade ago? I suspect it was a girly ride like this:
or maybe a smaller 12 or 16" version.
How she's 18, and this is probably unappealing. So explore rides that look as far from this as possible.
I'd probably recommend trying with a MTB style bike, even if you have to borrow one. Full suspension is not required, but front suspension will make the ride more comfortable, different to her old bike, again changing the perception. Yes, I know suspension will be slower than non-suspension, but that's not the goal here.
Later on you both can explore other kinds of bikes. Perhaps a 650b road bike if thats what she wants, or a rigid hybrid commuter.
Q3 Confidence - both of you just wear a helmet - a nice new one not a hand-me-down and not a rock climbing hardhat, not a baseball/football/sportsball helmet. Get it from a LBS and make sure it fits properly and is comfortable. She'll have something to say about colour, let her have her choice of helmet. I suspect she wasn't wearing a helmet a decade ago on the tennis court, another point of difference.
Another related thought - DON'T go overboard on kneepads and elbow and wrist pads and gloves etc. This sounds like a good idea, but it reinforces a perception of risk. Just ignore it unless she brings up the idea.
Q4 Where will you ride? To begin with, try an off-road bike path, either sealed or dirt/shingle.
Q5 What is your method? I'd start by showing off modern brakes and how much better they are than the old rim polishers of yore. At 7 she would have had minimal hand strength (ie too little to use the hand brakes properly) and a back-pedal brake needs planning to use. So play about with brakes while not riding.
Then scooter about a flat area (ideally anything that is not a sports court ) and definitely not near a net or chainlink fence.
Q6 Why do you want her riding? Is it to get places and be independent of parents for transport? Is it to get to and from school/work? That may help give a goal.
Q7 There are other types of bike too - you might build more traction and confidence by using a tandem or some other kind of multi-rider bike.
Also an adult trike might be a solution, but I wouldn't buy one to try... check if you can borrow one and see if it helps.
Q8 I expect you will need to lead by example. Try and have a goal to work towards, and you
Things to avoid:
Don't expect her to go fast, or to have much endurance.
I'd be staying away from all roads at the moment. Even empty ones.
Stay clear of any significant grades and heights. You want flat land, or a very minimal slope to help get going. Nothing above 2~3% gradient.
Totally don't talk about training wheels - In her perception that's "something for babies" so just don't go there.
Surfaces that are irregular may be a bad idea too - significant loose gravel or mud would be best avoided. Loose/dry sand is a terrible power sap, so is no fun.
Avoid motorised bikes - she has to build the confidence and ability before adding anything like this.
Trail Gators - She's too big for any tagalong bike.
Places to try
I don't know where you are, but here are some example locations in my city, which could be good sites for trying. You may have similar spots in your area, local research is required.
- Westburn Terrace - its a sealed street network which is inside a council park. There are no cars on those roads, but it has wiggles, road signs and intersections, a railroad crossing and a bridge.
A park - specifically a grassed park. This makes pedalling harder, but there's a perception of "softer landing" Another advantage is there may be gentle slopes landscaped into the surface. This will help to get going without pedalling, like a stride/balance bike.
A doubletrack like Bottle Lake Forest. This is an undulating area with no rise over ~3 metres, but its quiet and great for rides with the kids. No vehicles. The gravel is firm and compacted as well.
A beach - where the sand is damp and firm, but not saturated. You'll want to push the bike over any dunes to the firmer areas. Also, wash the bikes well after being anywhere near salt air.