Hi Mirjam,
in my opinion, the easiest way out is to insist with the bank: they do have records of all transactions, and they can make them available if you, their client, asks for it. If you have an online account with your bank, as most of us have, you can easily search for keywords in your account (i.e. AirBnB, rent, reservation, ...) and with a bit of work you should be able to retrace all payments. If that does not work, I suggest going to your bank in person, with your ID, explain the situation and get them to dig the archive of your account. The info is there.
Success!