You will need a SIM Card in order to open a bank account.
There are several telecommunication companies in Budapest. It is possible to find cheaper packages, however, it is better to choose from the below companies as they have the best service coverage in the country.
There are two types of SIM cards that you can choose:
Pre-paid: card needs to be preloaded with credit so that it can be used
Post-paid: card comes preloaded with credit, payment happens based on usage
To get a SIM Card you will need your passport and in some cases your permanent address. There are several stores downtown Budapest, they are easy to find. You can also ask AIESEC to help you.