Your particular question is a popular one. Here is a reference with 'Some Help' to get you started. In this recent Follow-up, I 'discussed' asbestos cement shingles. And you'll see that it's very easy to 'manage' but you still need to know what you're working with.
As for a specific reference on this topic, I haven't one. The only reason is because, as I discuss, you need to check with your local Municipality and your County and State Gov'ts on this matter. You can start locally and ask them if there are any County or State regulations they're aware of. If they say NO, then you're pretty safe to do what you need to do. Once you KNOW what you're working with, you'll see how it differs from the asbestos that they use to wrap heating pipes with in the old-days.
Now, as far as inexpensively disposing the shingles, the cheapest method I know of (in bulk) that you can do is rent a HAZARDOUS Materials Dumpster. It's a regular dumpster but you pay more because of, well, what you're throwing in it. The one I rented 3 years ago cost $375 in SE PA. That was for 1 week's rental. What I did was remove the shingles and 'stack' them on my property. Since my vinyl siding job took 4 weekends to do, I didn't order the dumpster until I was FINISHED the job. That way, the dumpster doesn't sit around 'doing nothing'. By waiting until you're finished to order the dumpster, you save yourself the $50 pre week EXTRA they charge you to keep the dumpster. (Such a waste of $$$.) I had 22 squares (2200 sq. ft.) of shingles! I just neatly stacked in on my property. It only took up about a 10' x 10' area, and they stacked up to about 4 feet in height.
BEFORE you order your dumpster, take an 'inventory' in and around your house, garage, basement, and/or property to look for other HAZARDOUS waste. I found an old bed, some concrete 'footings', rotted wood, junk insulation, roofing shingles, and more. I told the Waste Hauler how many sq. ft. of shingles I had, then I told him how much 'extra' junk I had too so he gave me a bigger dumpster. What a great way to get rid of a lot of 'junk'! AND, if you have some EXTRA room AFTER you fill it first, sell the 'space' to your neighbors. I sold some space to 4 neighbors and got $70 total from them! THey were happy to pay me a few bucks to get rid of stuff. You see, if you order the dumpster too soon, you may wake up the next morning and find 'stuff' in it already. Wouldn't that be nice of your neighbors to do while you're sleeping??! (Be forewarned!) Also, when the dumpster arrives, have 6, 3' long 2x6's for the dumpster to 'sit on'. My driver could have set that thing on a dime! The 2x6's help distribute the weight a bit. YOu want 6 because if you have a lot of weight, you may want to put 2 of them under 2 of the 4 corners. Talk to your hauler about this BEFORE he unloads it. (And be there when it arrives!) Try and get a dumpster that has a walk-in door at one end. Some are top-load only. Your 'stuff' can get real heavy if you have to lift it 5-6'! With a walk-in door, you can build a small ramp and use a wheelbarrow to 'move' lots of stuff into the far end of the dumpster. Then, as you get it filled, you can close the door and start throwing then.
I could go on and on. I think I'll stop now. Read the enclosed Follow-up and links for info. If you need more, e-mail me directly. Unfortunately, I'll be on vacation after this afternoon until Monday, 9/18 but 'others' will be around. You may want to start a NEW post because your post is getting buried already. My best to ya and hope this helps.