Have you actually changed BiaB to be MME, rebooted and then launched RB and tried ASIO?

Just curious.

ASIO is indeed a one man dog, and some drivers can switch between applications without problem while others don't seem to get properly 'released' for use in another program. I'm wondering if you are opening BiaB (or any audio program) and the drivers don't get properly released for RB. The most basic test is to set everything to MME, reboot (so Windows settings clear) and then try ASIO in RB.
That would determine that the RB/driver combo is an issue ..
or maybe a setting in the Oxygen is itself is errant. You said you changed everything in the computer to be 16 bit .. but if the Oxygen itself is set to be sending 24 bit you may have adjusted everything the wrong way.
.. then comes the 24/44 or 24/48 question .. some devices only support one of these.

Sorry, but lots of testing options came to mind when I read this.

I do not work here, but the benefits are still awesome
Make your sound your own!