okies, talking personal bathroom / toilet here, so you have a bag for disposal (not necessary in public bathrooms) and by cup I mean menstrual cup.

Women caught out generally won't ask for supplies unless they know you - the scenario is usually period came earlier than expected / unexpected bleedthrough / brain fart on being prepared so we're talking usually about a mess and it's a moment that's kinda shame charged by society to begin with. Don't feel pressured to cart about supplies just in case, but a little thought in a private area like your personal bathroom is always appreciated.

Sometimes a menstrual cup - or even a tampon - just will. not. sit. right. no matter how experienced you are with using them. So you go fuckit and swap it out for another product. Generally you want to rinse and UV sterilise / boil the cup but it's bit hard to do if you just nipped into a mate's bathroom. So a bag means you can rinse it, shake it off, stuff it in there, slip it into your handbag / pocket / whatever and deal with proper cleaning when you get home.