You can add a BIN, but the BIN disappears once you receive a bid on the auction. Although if it's the same listing as the one with the reserve, the BIN stays until the reserve has been met.
As you have to pay the reserve price fee whether the item sells or not and it's expensive i.e. £1 + 3% of the reserve price, it's best just to start your listings at the minimum price you are prepared to accept.
You should also change the method of postage on the ring. Normal post and Recorded doesnt' cover for 'valuables' i.e. jewellery, tickets, vouchers, money, stamps etc. and in any case only covers for up to £46. You therefore MUST send by Special Delivery Next Day. Keep the receipt tracking number/receipt somewhere safe for a minimum of 12 months as credit card chargebacks can occur months down the line.
Jewellery is also a high risk item that is targeted by scammers, so you need to be careful. Details here: