JC, You have a couple of problems. First, the shingles have to be removed by a lic. Contractor, because you will never be able to dump them on you own. If the shingles are still fully intact there is no hazard, the best thing to do is place vinal siding on your house. If the shingles are looking bad get them off asap, espically if you have young children. Asbestos removal costs are run by two factors one, the labor to remove the material, and then the very expensive dump fee for the shingles.