I don't know about the testing of the asbestos, but I can tell you my experiences of taking it to my local tip.
I had to dismantle a small shed that had an asbestos roof, so I made enquiries at my local tip. They provided me with bags to double-bag the asbestos. If I remember correctly, the asbestos went into a red bag first, then this went into a clear bag. I think they gave me 5 red bags and 5 clear bags, as they'd only take 5 bags of asbestos per customer, per day. Each day I dropped 5 bags of asbestos off, they provided me with more bags, so I could return the next day. I've absolutely no idea why they had this restriction ....anyway I got rid of it all in a few days, so no problem :)
This was approx 6 - 7 years ago ..... I've no idea if things have changed since ......