Drivers don't work that way if the program stays open.
Open a pdf and print it in color, then open another pdf, or reprint the same open pdf and the print driver will be selected on color.
That is working as intended and won't change. It assumes you want the last used settings.
Open a pdf, select color and print it, then close Acrobat / reader, open another pdf and when you print it will be BW, because you haven't changed anything it takes the driver defaults. It can't do anything else because the last used settings get wiped out when the application closes.
I can't think of an application for print that does not do this except Microsoft Picture and fax viewer, which holds last used settings forever and couldn't care less what the defaults are in most cases.
And since they are local installs not pushed from a Server/Group policy, the end user would have to set the preferences.
One thing you could try, and the outcome relies on bi-directional working in the driver, as well as the driver being compatible (Some will consider this a policy and not allow color to be chosen) would be to set it in CWIS to BW.
This usually works fine on the GPD, but often does not on the Native driver (YMMV). I have never tried with V10 drivers because I really don't like the V4 drivers (Neither the MS supplied Class 4 nor the Xerox supplied V4)
How do I set the default color to B&W but allow user to select "color" when needed -- then default back to black and white for next print job? I don't use a print server. All users are on Windows 10 using driver version 10.0.14393.0.