It is allowed in some areas to go over asbestos siding.
I would check with your local Building Department. They will also advise you of any health regulations you will have to follow as well.
It would be preferable to remove the the asbestos in the long run. You may have to disclose it in the sale of the house in the future. Even though asbestos siding posses litle to no threat to ones health in solid condition, just the mention of the word could cost you the sale of the house.
The cost of removal depends on where you live an what state and local regulations must be followed.
Again, your local Inspection Department should be able to give you a rough idea of cost.
If you decide to have the siding removed, make sure that you have a contract that states that the contractor assumes all liabuility for the asbestos siding and the proper disposal of it.