Diva cup

So I have been using the diva cup these past two days for my period. I wanted to try something besides tampons and I didn’t want to use pads because I feel gross in them. I wanted to know if there is any advice on how to get it out easier and it be cleaner. I have to stick two fingers inside my vagina to pull it out which then I end up having blood on my hands. And then you have to rinse it out and put it back. What if I was in a public bathroom? Is there an easier way to do this that I haven’t read or heard about yet? Please let me know thanks.