Answer:
No, only the A-C-E (the blue line) stops at 42nd Street-Port Authority Bus Terminal. Instead, walk through the tunnel that connects the 42nd Street-Port Authority station to the 42nd Street-Times Square station.
Then take the S shuttle train (color grey) east across 42nd Street, from 42nd Street-Times Square to 42nd Street-Grand Central Station. The 4-5-6 (the dark green line) stops at 42nd Street-Grand Central.
When the shuttle isn't running, you can take the 7 train (the purple line) instead, 2 stops, from 42nd Street-Times Square to 42nd Street-Grand Central.