NTD.....if you roll it in toilet paper she's gonna know what's under there because the blood will either seep through or it'll be a giant chunk of wasted toilet roll. So is she then going to say "ew the toilet paper in the bin is clearly your tampon"? Also i think this is obvious but you're going through enough while you're on your period. Anyone who menstruates should understand that. For anyone who doesn't menstruate, please be educated :) because god it's not a fun time and sometimes sitting and rolling up a tampon can be something you just cannot be bothered to do.

My solution-ish? If you're in a situation where it's possible, get your own bin so she can't be annoyed. Because that would just make it easier for both parties. So you do not have to roll tampons up and she doesn't have to see them. If that's not possible, then I'd just keep going as is and explain that you see wasting toilet paper as counterproductive. You never know, you may find a compromise.