Yes you need a card (ov-chipkaart or ov-pas) but you don't need to be a local to get one. You just order one online for 7.5/5 euros. You do need an address for it to be delivered to, but its valid for 5 years so if you visit the Netherlands again you can reuse it.
The "Dutch bank account" part is almost certainly illegal, by the way. Due to EU regulations they are required to accept any European bank account. It's called "IBAN discrimination", and the national central bank has a form[0] to let them known about it.