You can try calling some asbestos removal/disposal companies operating in the area where you live. They are sometimes happy to swing by (when they are on their way to the tip with another load of asbestos) and add your small quantity to the pile. They will usually charge a small amount for this service, but it is often less than the minimum charge applied by disposal facilities and spares you the concerns associated with transporting the material.
You can also hire an ‘Asbestos Only’ skip bin, however, for the small amount you are allowed to remove (under 10 square metres), this may be an expensive way to go!