Blue asbestos is quite a pretty rock. We collected a bit from Wittenoom for our rock and gem collection. Now that you have a bit you might consider sealing it with a bit of clear acrylic or keeping it in a fluid to prevent any chance of inhaling the dust.
Keep in mind that the majority of us have lived in homes with asbestos sheeting, asbestos roofs, asbestos pipes, asbestos fences, asbestos classrooms and the likes and very few have developed adverse affects from the dust. Our old house was made with material from old army huts so the interior walls, ceiling and roof were all asbestos and only the kitchen and dining room were painted. Mum, Dad and seven kids lived there for the first half of our lives and thankfully none of us have suffered from the asbestos at least to this day and we are all beyond 60 now.
I'm not saying it's not dangerous but if we are not altering it and creating dust then it's not as bad as the media reports over the years would have us believe. I would consider your little sample as a very low risk and perhaps many of the other rock samples we collect may be more dangerous. How many of us collect lead bullets and then go and grab a sandwich while failing to take precautions?
Phil