There are different banks (ad least in Europe) that permit “instant” transfers if they are done between their own accounts. (and usually free)
So I think that it can be useful if it will be possible to add a filter/search to see if there are offers that comes from one of these banks.
Maybe the easier way can be to add a search in the offers with the same ABI. The ABI is a part of the IBAN that usually match to the bank.
So, if the user will find that there are some offers from a bank that he knows that support instant transfer, he will be probably interested to use them. (if they are good with the exchange price)
Maybe this feature will push some users to open many other bank accounts if they are good to make faster trades 
I’m not sure if it the same for other bank account out of Europe, but I think that it should be enabled (the bank search feature) where ever is possible, even for other countries (maybe US, CHINA and elsewhere)
Than it can be good to prepare a table with all these banks that permit instant transfers, with their matching ABI codes (or other)
Example, some “banks” that permit instant transfers between their own accounts:
https://cryptocapital.co (it works mostly as a bank, the IBAN is dedicated, but it hasn’t the name/surname of the user)
https://www.wb21.com/
https://www.hype.it (mainly Italian)
https://www.chebanca.it (mainly italian)
https://www.unicredit.it (mainly italian)
http://www.poste.it/ (mainly italian)
Do you know others?
Sometimes the bank asks for the user-ID instead of the IBAN to make the internal transfer, so it can be useful to add a new field on the “Create new account” when the user chose to add a new bank account on Bitsquare, something like freenote-field.
The user can write something like this: “if internal trasnfers, my user-ID: 27359287535”