Not really. The correct way to dispose of asbestos is literally to put it in a garbage bag and send it to the dump. As far as a hazardous material it's only really bad for people. It's almost entirely chemically inert so it's actually far less bad for the environment than most of the stuff that winds up in the dump. Even ocasional exposure wont do anything to most people (not that it's good for you of course). It's mainly an issue if you work in an industry where you handle it every day.
I had to do some asbestos remediation in my house a while back (removing plaster filled with it) and I contacted the county about proper disposal. They literally just told me to bag it and huck it in a dumpster.