I wouldn't do it. If she knows how to do bank transfers and all that, why hasn't she set up a paypal account linked to her bank? Not as though it's hard!
Would say she's in the wrong here anyway as you specified paypal only. How did she get to bid anyway? I thought if you set up the auction paypal only, it wouldn't allow bidders without paypal accounts.
The kind of bank transfer makes a different too. Ordinary transfers take up to 4 working days. A BACS transfer will cost her (not sure how much these days but used to be around £30) and will be the same day.
you're not supposed to relist just yet. You are supposed to try and resolve any issues first. I would politely decline her offer of a bank transfer and say paypal is your preference but PO would be acceptable. If she hasn't paid within 7 days then you can start a claim but she can still pay (I think you get another 8 days before the case is closed) if she pays within that 8 days she is still entitled to get that item. If you have relisted it or sold it to someone else you can expect neg feedback. I've relisted too promptly and then had to pull a listing as the buyer paid up. It is worth starting an unpaid dispute after 7 days as the process is quite long and drawn out IMO
I've had a few months where I couldn't use my account. It got hacked and my bank account was emptied days before Xmas. I had to block my account and paypal said they wouldn't reinstate it without me faxing loads of personal data! I don't have a fax, xmas hols etc meant a huge delay plus they didn't refund my money for more than 6 weeks, think it was nearly 3 months to reinstate account, I could still bid on eBay though!
I read on one of the boards that someone did this and then posted the item - after 25 days the fake bank transfer was reversed. Her bank didn't even apologise - apparently it can take a long time for them to be confirmed.