I am not a remediation specialist, nor licensed to test for this stuff or whatever, and I'm not a lawyer either so please don't take any of this info as legal advice. Just sharing some of my experiences as far as my interaction with it throughout my real estate career.
That being said, here is a few things to take into consideration from what I have seen and been told...
Asbestos acts like a binder of sorts... Glue like characteristics at the molecular level if you will. This is the reason it was so widely used, and in so many products. Combine the substance you want to create a product out of with with asbestos and you can shape it any way you want etc etc.
Here is an example of the extensive list of products that used asbestos for production.
Asbestos Gaskets
Asbestos Sheets
Cigarette Filters
Electrical Cloth & Electrical Panel Partition
Fire Proofing & Prevention Materials
Fume Hoods & Laboratory Hoods
Plastics
Vinyl Products
Textile Cloths & Textile Garments
Construction Products
Adhesives and Gold Bond Adhesives
Construction Mastics & Gunning Mix
Ductwork Connectors & Flexible Duct Connectors
Floor Backing & Drywall Taping Compounds
Insulation
Zonolite Insulation
The whole point being that first off this is not necessarily a product that you can see with the naked eye for the products that contain it and those that don't.
I have an addition in my house that had popcorn ceilings, and the addition was done in the 50's. When I bought it, my inspector told be that the ceiling was "obviously" containing asbestos, and to just leave it alone if at all possible, but that if I were to mess with it I should either cover it up like you are planning on or have specialists come in and remove it at a potentially very high expense. My father (40+ years of construction experience) backed up what the inspector said as well, but just told me if I left it alone it wouldn't be a big deal or something I should worry about.
Only thing is that my ceiling actually DOESN'T have asbestos in it...
A few years after becoming a Realtor I needed to remodel my back room. Having learned a lot more about the subject I had a little better plan of action to work with. I went and got it tested, and it turned out that there was NO asbestos in my 50's popcorn ceiling. Imagine that! I was really excited, as opposed to having a several thousand dollar bill to remove it all in a safe manner so my child could be safe, I just drywalled a new ceiling for $150 bucks. Spending a simple $25 bucks was a lifesaver!
The thing is, most people don't even really know how easy it is to test for it and check it out, all most people know is that the specialists are really expensive. If I were checking it on my own house etc etc I wouldn't rely on a lowe's test or whatever, I would go straight to the horses mouth. There are labs out there that service exactly these types of things. The one that I use in Salt Lake is called ALS Laboratories.
http://www.alsglobal.com/en/Our-Serv...ity-Laboratory.
They have labs all over the world, perhaps they have one where you live? Testing is really easy, they just need about a golf balls size worth of material to test it. They will go through and check it to the parts per million level etc etc.
Lastly I will touch on another thing I never knew but was fascinated to learn.
FWIW...
Asbestos is actually a blanket term that encapsulates 6 totally different products:
http://www.asbestos.com/asbestos/types.php
It is important to understand what you are dealing with if in fact you DO have an asbestos situation to deal with. The different types have varying risks and health impacts depending on which "animal" you are dealing with. This stuff is all important to assess if you are planning on dealing with asbestos, and all the more reason to get it tested professionally. Also, realize that cutting out the chunk you are planning on testing is an at your own risk situation, and that perhaps if you are not comfortable with that risk you should have the sample removed from the ceiling by a professional.
Whatever you do, DON'T PAINT IT. If popcorn asbestos ceilings are painted they are significantly more difficult to remove. It's the difference between being able to spray the ceiling with a squirt bottle and leaving the room while it falls to the ground on its own, versus having to scrape it all off by hand.