For chasing I use a Metabo chaser with Trend M class vac, plus fitted face mask. When sweeping up I try to damp down the dust as best as possible.
If drilling ceilings is necessary I check the asbestos report, then if anything nasty is present I believe company policy is to suit up, fitted face mask, rubber gloves, dust sheets and H class vac, the the dust sheets are double bagged and put in the asbestos bin at the yard.
I believe some people apply shaving foam to the area to be drilled to catch any falloff.