(Good luck waiting for 'Bob' to answer ...) Anyway, I can tell you from personal experience what I've encountered in the last year. I live in SE Pennsylvania.
2 years ago, I checked into the laws regarding asbestos, cement siding. Last year, I did it again because 2 years ago, other 'things' prevented me from doing the job. Well, what I found out last year and what I found out 2 years ago was the same thing. I started at the EPA. They told me that there wasn't any current law preventing the owner of a single family unit from removing and disposing asbestos cement siding. So, I called the PA EPA. They told me the same thing. So I called my county seat. They, too, told me the same thing. So I called my local township. Low and behold, there was no law. So I was free to do what I liked. BUT, almost EVERY level of gov't told me that there's chatter about regulating this stuff. Nothing official; just talk. This meant that I'd better get started ...
Asbestos, cement siding is non-friable asbestos. (I'm assuming this is what you have.) Less than 1% of it contains asbestos. Non-friable means that the asbestos doesn't become air-borne when you crush it (the siding) in your hand. Because of this, the hazards compared to friable asbestos are slim to none. You, basically, don't want to 'smash' the shingles if you don't want to increase the small exposure hazard. Because it's solid, because you're working outside, because you're gonna be careful NOT to generate air-borne asbestos, and because you're gonna wear long sleeves, pants, gloves, and a dust mask, you're pretty safe in my mind to do the demolition yourself. Rent some scaffolding so you can 'stack' the stuff as you work down the wall. It's well worth the $$$. (I did 22 squares in 60 hours.) Now, as far as disposal, I opted to have it properly disposed of. I could have put it in the trash a little at a time but I wasn't comfortable doing it. So I rented a dumpster, loaded it up with the siding shingles, and paid to have them properly disposed of it. I DID re-do a roof on our addition and I did re-insulate a crawlspace too so the dumpster did get more use. I even emptied out the shed and basement of unwanted junk. And since I had some extra room, a couple of neighbors were happy to pay me a few buck to be able to throw some junk of theirs in it! (That was AFTER I filled it with my stuff first.)
So this is my experience. I do want to add that you don't want to put any other form of siding OVER your current siding (assuming it's asbestos, cement shingle). The shingles will 'shift' underneath, you won't have a smooth surface to nail the new siding too, and you MAY void the warranty on the new siding! Yes. I suggest you remove the old siding and, depending on what's underneath, put up an OSB or a 1/2" insulation board (foil side in because you don't want the sun creating an oven between the insulation board and the new siding.) While you're at it, you may want to consider putting in new/additional electrical outlets for the outside, along with new/additional hose connections too. I even taped my seams. I saved quite a bit of $$$ doing the demolition, plumbing, electrical, and finish work. I preped and painted all the trim on the house, then had it capped with aluminium. I now have a completely maintenance-free home when it comes to painting! Don't cap rotted or unprimed wood. It needs to be protected with some sort of primer/sealer first. There's lots more but I've rambled on long enough.
Best to ya and post-up if you want more info. Or e-mail me directly.
PS. One of the laws that's currently on the books in many states (and making its way to the rest of them) is a Seller's Disclosure Law. When you go to sell your home, if you cover-over your asbestos siding, you MAY have to disclose what's underneath to your buyer. Try to sell your home then! (You could be sued if you don't disclose.) Again, my free advice is to remove it first. TAKE PICTURES before and after for proof. Oh, and if possible, select a light colored siding. White, gray, tan, baige, etc.. The darker colors absorbe the sun's heat and this can assist in its aging. Wharping is something you need to be mindful of. Dark colored homes are actually harder to sell too. Just my extra 2 cents. :)