Once bitcoin will be mass adapted it will be easy for banks to make transaction like us dollar or any fiat currency in the economy. Banks and bitcoin or cryptocurrency will be a big legit transaction worldwide once adaption is in effect.
Of course adoption into businesses is the key fact for bitcoin to develop as a currency and with that other things like usability, acceptance comes easily so banks will definitely combine there core business with bitcoin but without adoption nothing can happen but considering today trend bitcoin has a good adoption rate than the past because earlier it was mainly used as a trading commodity rather than using with business processes but now some companies are combining bitcoin with there core transaction systems which is a good thing