These shingles are deemed Non-Friable. This means that if you 'crumble' it in your hand (or try to), it doesn't become airborne. It's when the asbestos becomes airborne that you can breath it in AND you can get 'sick'.
WIth that, even a semi confident homeowner can remove the shingles themselves w/o much risk. (You don't want to 'throw' or toss them where they'd end up breaking.) You stack them in the driveway and either have them professionally removed or make 'arrangements' w/the Pro about disposal.
So, I suggest that when you get your bids, you have REMOVAL and DISPOSAL prices given separately. Then, you can decide what you want to do. Bottom line - As Jason said, I'd have them removed. You DON'T want an uneven 'surface' to install the new siding on. Once it starts breaking and falling down BEHIND your new siding, you'll get bulges and stuff. Also, you should get a copy of the MFGR.'s WARRANTY from the Pro FIRST before you sign. THis way, you can learn what 'things' would VOID a Warranyt. (NOT having a smooth, flat surface is usually one of them.)
If you need more guidance, post back. My best to ya and hope this helps.
Jay J -Moderator
PS: Another reason to remove them is, as you can see from your initial 'understanding' of the shingles, the talk of asbestos in or outside the home conjures up all kinds of thoughts. A little research goes a long way ...