She needs to prove it's NOT Ostrich, and with that - you'd only accept a certified notarized statement from a reputable antiques dealer. Don't let the buyer hassle you; probably buyer's remorse has set in. As far as you getting it authenticated - check with a couple of antiques dealers and see if they can do it or can recommend somewhere based on what you've told them. Obviously you can't do it with the bag now since you no longer have it, but if it ends up coming back, that's what I'd do. There may be a cost involved to authenticate - and maybe next time you can describe the bag as 'appears to be ostrich' rather than 'ostrich'.
If you don't feel like dealing with all this, gladly accept the return, refund her money, and move on. It may STILL get you a negative feedback, but you can reply to that and any future buyers won't have a problem with that.
We're moving into 'ebay'/authenticate-this territory, so this thread might be moved - don't be surprised if it is.
*Edited to add - I do see from your original auction that you stated in response to a question that you 'believed it to be' ostrich - that's as good as it gets, m'dear - let the buyer file. You answered the question and it was still purchased, you can't do any better than that.