Make sure that you get a real company,no cowboys.After the sheets had been removed it is essential to clear ALL dust from the place below the sheets,for example the roof battens/laths and from the vapor barrier.The best way to do that is with the aid of a vacuun cleaner that has an anti allergic filter,a so called pollen filter.The vacuum cleaner incl.its filters will than be hazardous waste itself,it is not destined for the metal/electrical recycling bank!
The protective clothing is not just a cardboard mask and cheap leather gloves.Get the best equipment available.The masks have to be marked with the slogan "suitable for asbestos dust" or at least with an CE2 symbol for the small piece you have.Again:all your protective clothing is not suitable for further recycling in the cloth bank for example.It will be hazardous waste it self.
My advice is to get a contractor to do the job,one that is licensed for that particular work.And demand a bill from the contractor that states exactly what had been done and where it went , incl. the bill-or a copy-of the waste handler or the dump.It must state what sort of waste was accepted incl.the quantity.
Here in Cork I have witnessed how the yellow plastic bags (determined for asbestos waste) had been dumped in a wetland and been covered with rubble.Opposite Little Island(Henkel) at the container terminal ,a 30 seconds drive from the Lee tunnel to wards Midleton on the left.This practice is still going on,tens of thousands of people can see it every day from the road .But officials won't look at these matters,the container terminal got subsidies ,it is so important for the nation after all that even the residents won't complain....