Many of the early bikers were veterans of the Second World War. A very central event to early biker culture was the Hollister riot. During the summer of 1947 a motorcycle rally was arranged in Hollister, California, by the American Motorcycle Association. A handful of bikers got out of control and started causing a commotion. In reality the "riot" amounted to very little as soon as the media got hold of it, it was blown up into ridiculous proportions. The Wild One, a 1954 film starring Marlon Brando, is loosely based on the Hollister riot, but it isn't very factual. That said, bikers have been regarded as "rebels" pretty much from the start.

If you are more interested in outlaw biker culture, I can really recommend the works of Sonny Barger, a founding member and former leader of the Oakland chapter of Hells Angels. This man is a part of the original Hells Angels, so to speak. His autobiography, Hell's Angel - The Life and Times of Sonny Barger and The Hell's Angels Motorcycle Club offers great insight into his life as an outlaw biker, though I strongly suspect he may have omitted much of the criminal stuff.

In addition to the other answers, one must consider the changing demographics post-war. It was only in the late 50s-early 60s that a generation was emerging who had disposable income, and who were fairly large in numbers. Those buying motorcycles were generally speaking those too poor to have cars, so as young and fairly poor people they were a natural target for a hysterical media. Throw in every parent-of-a-daughter's horror at the possibility she might be attracted to a biker and you have a real connection. And motorcycling was very very dangerous at this time.

So at this time vehicles were becoming more than just basic transport and the 'lifestyle' aspects of vehicle ownership were filtering down. One can see in the popular motorcycle press from the 1950s to the 1980s a constant theme of motorcyclists as responsible citizens, with the hooligans as an undesirable minority.

Up until World War II this whole impression seems to have been absent, probably because any vehicle ownership required a person to be pretty affluent. If you could afford to own and use a motorcycle for recreational purposes you were probably very wealthy anyway.