This isn't true. In my city, you take it to the dump and specify that it is asbestos. They charge a dollar more and tell you to put it in the special asbestos area. No laws against it at all.
Asbestos is way overworried about. It has almost zero chance of harming you. At the very worst, there is a slight uptick in rare cancers from people who breathe it in daily during work (mining, manufacturing, etc) and only then if they are also a heavy smoker. Anyone else is fine with occasional exposure. Just wear a dust mask, wet it down, and report it as asbestos when you dump it. You'll be just fine.
http://www.atsdr.cdc.gov/toxprofiles/tp61.pdf
"Asbestos-related lung diseases (malignant and nonmalignant) or signs of these diseases have been reported in groups of occupationally exposed humans with cumulative exposures ranging from about 5 to 1,200 f-yr/mL.
Such cumulative exposures would result from 40 years of occupational exposure to concentrations ranging from 0.125 to 30 f/mL. Currently, U.S. OSHA regulations require that workplace air concentrations of asbestos not exceed 0.1 f/mL.
Exposures of this magnitude are usually not encountered by the general public...  
Although there is considerable uncertainty in the estimates, EPA calculated, using a linear, no-threshold model, that
lifetime exposure to asbestos dust containing 0.0001 fibers >5 μm in length per mL of air
could result in about 24 excess cancer deaths (lung cancer plus mesothelioma)
per 100,000 people."
In other words, you'd need 40+ years of exposure above the OSHA asbestos regulations to begin to have a chance of possibly having a higher incidence of an already rare disease. In numbers: after 40+ years of heavy exposure you have up to a 0.004% additional chance of death.