One of the earliest pop culture reference to the bike that I've discovered is in comics.
The Family Cat released the album Tell 'Em We're Surfin' in 1989. It doesn't sound the way the title suggests, but it does have that '80s indie punk pop thing going for it. The LP did have a couple of good tunes, but never really broke any new ground. One thing firmly in its favour, however, is the remarkable opening instrumental, Albert Hoffmann's Bike (sic). It's like The Ventures reimagined by Buzzcocks, all trebly guitars and staccato rhythms, and sounds as good now as it ever did.
So, any earlier references I should be aware of?
The Family Cat - Albert Hoffmann's Bike