No sharps bin

Whilst we wait for our <a href="">IVF</a> paperwork to go through, we are doing a medicated cycle. 
I do an Ovidrel trigger pen tomorrow, and have just realised I don't have a sharps bin/container. 
What do you recommend? Is it okay to put it in the sharps bins in public toilets? Do I just dispose of the removable needle or the whole pen?