There are addons like bagnon that will help with this, when it gets fully functional. 
Right now the movable bag windows works with a combined view, but the bank will not open with it running. It has worked fully earlier but things are still changing therefore addons break and sometimes break basic WoW functionality.
Note edit: 10/28 Unable to find switch for multiview in bagnon. Would have sworn that I have used a version that supports keeping the bags separate but movable.
I never really liked bagnon. I can’t tell you why now because it’s been a while… The one thing I know about bagnon that I did not like was that it forces everything into one bag which, as I said above, I do not want and do not like. I used to use BankItems but that is no longer supported and won’t work with the new version so, I don’t know. I may have to search around for a new add-on. But, right now, more than half of the add-ons I was using are non-functional.
How about making new drops go into the bottom of your bag. I used to reverse bag slot order with bagnon and i had found a fix with the prepatch that worked (https://us.battle.net/support/en/article/45020) but as soon as the drakes dropped Tuesday it doesn’t work anymore or at least with brand new toons.