@KnobScratcher pointed this out, but it's worth repeating: In the more populated areas, your problem will be disposal.
There are a potentially huge list of issues here. The simplest and easiest thing for you to do is to take a sample and send it off to be tested. In the U.S., your municipal or county government will be able to provide you with information about where to have it tested. (Typically, the inspectors will know a lab, or know someone who did it once and put you in touch with them.)
This test should be pretty cheap, no matter where you live. Asbestos isn't that dangerous in a lab setting, nor all that hard to recognize.
Once you know it's asbestos, think about how you're going to get rid of it. If you pay someone (which will be expensive), they'll haul it away. But if you take it down yourself, what are you going to do? It won't be trash - it's construction debris.
Depending on where you live, you might find it's as expensive or moreso to pay someone to dispose of it as to pay a contractor to remove it. This is because "dispose of these unknown bags" is riskier than "take this down, and dispose of it knowing what it contains."
Finally, keep in mind that there are a lot of people working in your refuse chain. Trash men, landfill workers, etc. Don't just "hide it" in the trash and try to sneak it onto the weekly truck- you'll be endangering a lot of other people if you do.