According to the 1912 Sears Catalog, a men's bicycle could be had for 11.95.

This site, which lists a government study, reprinted in the Ladies Home Journal lists the average wage for a steel worker as $630.

Assuming that the $630 is take-home pay, he would make $12.11 a week.

A bicycle wouldn't be a simple purchase, but it wouldn't be monumental either.