The motion of a binary system about its center of mass causes the proper motion of the two stars across the celestial sphere to wobble. If only one star can be seen, the presence of the unseen companion can still be inferred by its influence of the motion of the one that can be seen.
This may be illustrated by using the buttons in the Sirius A+B to hide the orbits and to hide Sirius B. The corresponding motion is what we would see for Sirius A if it did not have proper motion on the celestial sphere. This motion, coupled with the proper motion of the center of mass for the Sirius system, gives the wobbling path noted above.