Unfortunately eBay recently introduced a "site improvement" that resulted in all buyers having to provide credit or debit card details if making a Best Offer, and they automatically enrolled all sellers into the new scheme at the same time. Therefore the end result is that a lot of sellers don't even realise that they've been signed up to the scheme.
In light of the above I would advise you to send the seller a message via the Ask Seller A Question option, explaining what has gone wrong and stating that you would like to make an offer on an item. Ask the seller whether he/she would be willing to deactivate the feature that eBay have imposed on sellers requiring buyers to provide card details so that if the offer is accepted you can choose to pay with cash when you meet the seller to collect the item.
If the seller is unaware that he/she has been opted into this scheme and agrees to deactivate the automatic payment option then once he/she lets you know that the feature has been disabled try to submit your offer again. In this scenario you shouldn't end up being forced to provide your card details for payment and can contact the seller again to make arrangements for you to collect the item should your offer be accepted. Under these circumstances you ought to be able to proceed throught Checkout, selecting the option that says "I will pay the seller when I collect the item" and then pay the seller in cash, exactly as buyers used to be able to do with Collection In Person Only listings before eBay messed it up.
