In that period, many U.S. towns and cities required registration of bicycles (theoretically to aid in recovering them if they were stolen), and frequently the fact that the bike was registered was shown by the display of a small license plate (I had one on my bike when I was a child). Other political entities required that the registration number be engraved (scratched) on the bike's frame (I had this on another of my bikes as a child, in a different state). This requirement was only at the local level, and was not part of the state-wide requirements for license plates on automobiles.
I guess to add on to my question. Were bicycles considered like cars back then?