The procedure for the mobile version is to input your phone number and birthday on the login and you get a popup on the phone (via the gsm network and sim toolkit, not ip) to input your password along with a short phrase like "pink bridge" so you can verify that it was the web page that sent it. This also works with a lot of credit cards for paying online via 3dsecure.
It's become so common that a large majority of our customers (I work in a bank) are using this as the sole mechanism of identification.
(And yes, for the non mobile version of BankID you can paste the password!)