Megabytes per second was (as you will remember) on parallel comms interfaces where there would be one (8 bit) byte of data sent across 8,9 or 10 parallel data lines with two providing some form of parity capability or with 16bit byte systems across 18 or more data lines. Plenty of ambiguity there.
And definitely "bits" is the only non-ambiguous way. Even kb & Mb are ambiguous!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
M H C
taurus excreta cerebrum vincit