We recently adopted a stray border collie/lab mix that showed up lost at my dad's house. His Newfoundland attacked her with full intentions to kill her. We were not able to locate her owners and she couldn't stay at my dad's.
She seems to be very intelligent and well trained. She usually only needs to be corrected once. She doesn't have a strong herding instinct and works very well with the kids. The only problem, she is very sensitive and if she feels neglected or thinks she is abused, she jumps the fence and takes off. We gave her a bath and found out she hates water (felt abused), off she goes. She also will take off if I fail to walk her at least twice a day. We have a 1/4 acre yard, she has plenty of room to exercise and she prefers to be outside.

She never goes far, and seems to return on her own, but in a busy city, this is dangerous. She knows her boundaries and only takes off if she is punished or doesn't get her walks.
Would an invisible fence help keep her contained? Or is there something I can try with training. My fear with invisible fence is that she would perceive it as punishment and take off for good.

Thank you for your suggestions.
She is a mix of one extremely active breed that really isn't suited for most homes and a moderately active one.
She needs a lot of exercise, it sounds like when she gets the exercise she needs she has no inclination to run off. I'd bet she left her old home and made her way to your dad's b/c she wasn't getting the exercise she needs, few Border Collies do.
If you cannot devote the amount of time needed to fulfill her exercise requirement you should think about finding her a home where they can. Agility/obedience competitors, joggers, cyclists, anyone who spends a great deal of time doing an activity that can include a dog make the best homes for Border Collies, IMO.
You could probably force her to stay on the property without giving her the proper amount of exercise but the frustration will express itself in a variety of nasty ways barking, chewing up the house, going to the bathroom in the house, digging, self-mutilation, etc.

Kristen &
Kali CD, CGC, TDI, TT
http://www.kristenandkali.com
Would an invisible fence help keep her contained? Or is there something I can try with training. My fear with invisible fence is that she would perceive it as punishment and take off for good.

You don't really know what your dog is feeling. Lots of dogs don't like baths. Whether or not your dog is feeling abused when she gets once is a matter of conjecture. The same is true of why she jumps the fence. She could feel abused or negelected, but more likely she doesn't perceive the fence as something designed to keep her in the yard. Since she can jump it easily, she might think it is a fun hurdle that you put there for her amusement.
The fact that she responds to you, learns easily and only needs to be corrected once speaks volumes for the fact that you already have a good relationship with your dog. Dogs that feel neglected and abused aren't that well behaved. Those dogs just act scared all the time and can't learn well.
Border collies and labs are certainly 2 dogs that can benefit from lots of physical and mental exercise. That will certainly help, but your immediate question is about using an invisible fence in conjunction with your physical fence to keep her safely in your yard. Assuming you're not just throwing her in the yard and expecting her to stay there amusing hersef, I think it is a good idea. Here's an old post of mine on the subject: