If you're going through insurance - just do research on local Toyota dealerships with collision centers that's located elsewhere. That way you know you're going through a body shop that is certified by insurance (i.e. Toyota dealership with their own collision center they actually run themselves, not a third party) & they'd do a good job on repairs. They'll probably overcharge her insurance like crazy but that's on your neighbor for backing into your vehicle. Her rates will get jacked up regardless.
If you're doing it out-of-pocket to help her out avoiding insurance since you're neighbors and want to stay on good terms, (who wants to deal with ******* neighbors on a regular basis right?!) take it to a Toyota dealership and have a quote in writing. Make sure they inspect at the rear bumper to ensure no deeper damage exist. Tell her to pay this xxx much according to the quote and you'll give her a statement saying you release her of future liabilities regarding the damage. If she gives you crap for the estimated quote then tell her it would still be the same as if it's through insurance. You're doing her a favor by giving her an opportunity to pay out of pocket first.
As a general rule, one should always go through insurance in event of an accident but if it's a neighbor or someone who i'm familiar with, I'd offer to do out-of-pocket repairs pending inspection of damaged parts only if it's a minor accident. Otherwise if they cannot afford the quote i.e. $1,000 out of pocket to repair/replace bumper then I'm going through insurance. That's just me though