OK, I'm going to just throw this one out there. Not as a recommendation, but just as a reminiscence of how I used to manage this in school, since people are talking about school and college.
I was in Primary School (ages 6-13) when my periods started. I'd change my sanitary towel in the school toilet but there were no sanitary bins provided because I guess our school was in denial about the fact that a 12-year-old can have a period.
So I'd just wrap the used pads in toilet paper and put them in my pocket, then I'd later transfer them to my school bag so that I could take them home & throw them away there. There was no way I could bring myself to throw them away at school in a public bin where everyone could see what I was doing!
All of which was pretty much doable until I had a rather nasty incident where my English teacher didn't believe me when I told her I'd left my homework at home one day, so she called me up to the front of the class with my school bag and she tipped the contents - including a used sanitary towel which had unravelled from the toilet paper - all over the floor in front of my entire class. That would be bad enough for anyone... but I was severely dysphoric about my periods so it was extremely traumatic for me.
From that day onwards, I couldn't use sanitary towels at school. I used to roll up several sheets of toilet paper & put that in my underwear instead. Of course, the risk was that I would bleed through to my uniform but I'd just use thicker piles of TP on the heavy days.
That way, I could just flush & replace it every time I used the toilet, and there were no suspicious noises or anything.
Oh and that English teacher? I posted this story on our school's website a couple of years ago, and she contacted me on Facebook to apologise. We're now friends on FB.