Same here. Me and a friend found some corrugated (what I believe now to be asbestos) dumped in a field and we had a bit of fun karate chopping it etc. From what I have read the grey corrugated stuff is not as harmful as other types and its more people who have long exposure to asbestos that are at risk.
Enjoy the asbestosis

To the OP - wrap it twice in polythene sheeting and duck tape it shut. Take to the tip. Wear a mask, wet down the area if you think it might break (won't stop the dust just limit it) and you'll be fine.
As there's some in the loft are you sure there isn't any more lurking in the walls? It's when you start drilling and release into the air when you get the probs!