Have you ever started a horse? I'm guessing if you are asking as to how to start this one, that you haven't?
If you haven't, then I wouldn't recommend starting this horse by yourself. If you're still willing to do it, then get some material because it's going to take you watching trainers techniques (if not in person at least through videos) as to how to start.
I'd recommend getting Clinton Anderson's ground series. He goes step by exact step. Awesome stuff.
What I do when starting a horse is using his ground work:
halter and lead line (with a horse like this, I'd use a 22 ft lead)
desensitize the horse to be able to be approached and touched and rubbed all over with your hand and the halter and near the feet with a whip. get to where you can touch the horse anywhere. this will take a lot of approach and retreat (depending on how spooky the horse is)
next I'd start with hips over. disengaging the hips. both sides. These hip exercises are what will stop the bolting 100%.....then work up to sending the horse in a half circle and stopping the horse via hip disengaging.
there's loads of steps to it, so really if you've never started a horse, you will need to get some material at least...better yet, work with a pro in person. it's not enough to just say do this and that through posts here,....because you've got to think about this....you will be putting the basic foundation work into this horse.
that means, that if you are not confident in your skills and get scared easily if the horse reacts big, then you will be training the horse to have a lot of bad habits that then you or someone else will have to change and on top of putting in good training. So, double duty for mess ups.
I'm just saying that to show that it's not something you can just do in your spare time, it's a real commitment to start a horse. getting the timing and feel right so as not to cause bad habits. as is, she's learning that she can lock her body and pull away from you (which is normal prey instinct fight or flee when scared)...so if she does this enough times, you've taught her to bolt on a lead. so, then you'll have double duty to fix that and put in good leading manners. double duty.
Frankly, I think these people are taking advantage of you. They don't pay for training and you do all the work. AND they have already proved that they are not honest with you. They just sound like mooches to me.
I'm not saying you can't do it. You can. Hell, if I can do this stuff, anybody can. But I'm saying it's a big commitment. Because the horse's first experiences are extremely important and will shape the horse for the rest of her life. Bad habits are retrainable, but they are hard to break.
Then I basically, ran back and forth a bit after her in the arena just to wear her down a bit so she'd be manageable.
This isn't something you want to do. You're chasing her and acting like a predator which triggers her prey response, and can make things more difficult for you later on. You aren't going to wear her down, you're just going to teach her to be scared/wary of you.
Also...I didn't see anywhere in your post as to the age of this horse. If the horse is less than 3 you definitely don't want to do anything like running her around hard. that's hard on her body (and doesn't do anything for training). I wouldn't recommend running any age horse like this, actually. Doesn't train em for anything other than to run away. I've fixed many horses who were chased who then turn out to be hard to catch.
Honestly, I would recommend against starting this horse by yourself. Don't mean to sound like a downer,....but I just don't get a good feeling about any of this.