I get a book about urban legends that is older than the intenet. They only study a half a dozen of these, but quite in depth, and in particular the way they spread. They could spread quite quickly by word of mouth, or, in the case of UL related to a safety hazard, for instance the disney decals supposed to contain LSD, they were photocopied and distributed.
They tracked closely the spreading of this one in France, and the first known appearance of a photocopied document warning about the LSD decals (IIRC in the meditteranean port of Marseilles) was a direct translation of one of these warnings circulating on the american west coast. So, the UL was directly imported in France from the US.
These copies were from time to time rewritten (at some point, people had to type again the text, since copies of copies of copies become impossible to read, and some of them change some of the content for some reason of their own), and sometimes printed on some official looking paper (an hospital letter paper, for instance). People with good intents would want their friends, colleagues, relatives to be aware of the “danger” and would distritibute them. Someone in a company (the guy in charge of health issues or maybe the worried owner) could make sure that all the employees would be warned, and so on. As a result, the UL spread extremely quickly all over the place.
Others ULs would just spread orally. One of these case was studied. The UL (about the abduction of young women in cloth stores) appeared in some town in central France, and within days all the town was “aware of the danger”. Very quickly, the UL “contaminated” other french towns, loosing a little accuracy (originally the UL was about some specific shops, and in other towns, it became either unspecified shops or cloth stores owned by sephardic Jews).
In this case, the UL appeared and spread quickly, but I would want to point out that some UL are extremely old, hence had all the time in the world to spread everywhere. For instance, the “ghost hitchiker” story is a variation on an old tale (a farmer coming back from the nearby town market with his cart pick up a woman who warn him about an impeding danger, a fire, for instance. He latter discovers the unknown woman is long dead. Change the cart for a car, the fire for a road accident, and you get the modern version of this ghost tale). This story has probably been told for some thousands years. Similarily, the story about a guy who drink alcohol from a barrel where, unbestknown to him, a human corpse is kept was already been told during the middle-ages, and , I would suspect, probably earlier.