As far as I know there are no options, the aim of the anti money laundering laws over the last decade or so has been to prevent exactly what you want to do.
Either it's a scam or she wants your name, and bank details, for some reason, or she doesn't want to deal with you and is making payment as difficult as possible, so it's your 'fault' for unreasonably wanting to preserve some limited amount of anonymity.
I'd move on if I was you. She's being too awkward. Plenty of SPs take cash.
ETA - the whole absolute bargain thing you've just posted, red flag, especially combined with the bank transfer. To me anyway.