I had a sharps bin on prescription when I first got my meter but I was never told what to do with it when it was full. My OH works at a hospital, so when I remember, I give them to him to put in the sharps bin at work (I'm terrible at remembering to do this so have quite a lot at home).
I also put the little 'hat' on mine and I think they are quite harmless like that, its not like they are syringe needles. The likelyhood of a bin man getting an infection from them is minute.
I was thinking of putting them in an empty 4 pint milk bottle and putting the lid on and putting them in the bin. We have large wheely bins, so the rubbish isn't touched by the bin men, but I would have thought inside a bottle, in a bin bag, the seagulls would have a hard job getting to them.