Like Risa suggested, it's best to spit it out.
I once heard the reasons for it, which had to do with the bug never getting out of the system.
Since I heard it being best to spit it out, I also use a tissue, toilet paper, or directly into the drainage systems! Strangely enough, between leaving the house and reaching the train station, there are NO trash cans, so I stopped spitting into a tissue (since I end up carrying it) and started spitting into the drainage systems on the way. I just try to make it a little descrete when there are ladies nearby, but unlikely at 7 am.
I also check the color, and whether any blood was mixed in or not.