C.V.
I usually carry a travel pack of unscented baby wipes. Dump and wipe it out, put it back in. I also like to have the wipes to clean my hands if needed.
You can also dump and just wipe it out with some TP in a pinch. Clean it in the sink the next time you get a chance.
The other option is to have two. Dump and wipe out the one you're using, and put the other one in. Bring the one you just used out and wash it out, put it in its bag and it's ready for the next switch. Don't forget to boil them both at the end of your cycle.
It seems kind of icky and complicated to the non-menstrual cup user....but trust me, it's MUCH better than having to buy tampons or pads every month, and once you get the hang of it, SO much cleaner.
Let me know if you have any other questions!