Technically people travelling on school concession cards are required to give up their seats to full fare passengers. In saying that though, you shouldn't have to give into a bully like that woman. Back in high school, I probably would've been shocked enough to just give up the seat, like the students you saw. It's a level of rudeness that takes people aback. Of course, if it happened to me these days I'd probably say something sassy like, "You gonna say 'please'?" It'd put her in her place if she had to be polite to me. If she'd refused to use manners, I would have refused to give up the seat.
I have an incident that kind of haunts me because I was so shocked by it. I was walking home from school with a friend one day, and a middle-aged man was walking the opposite direction. The footpath was too narrow for three people, and I couldn't move over without forcing my friend into a tree. The grass was firm and flat (it was almost summer - no mud or anything) so I figured the man would just walk on the nature strip for a few paces to pass us. Instead he walked right in the middle of the footpath, and rammed me. It was obviously intentional, and he'd braced himself right before he hit me. I said sorry automatically even though I knew it wasn't my fault, and he abused the fk out of me. My shoulder was really bruised, and I was pretty shaken.
It really sucks, but there are a lot of lowlifes out there. A lot of adults will bully school-aged people because they have sad lives, and they don't have the guts to pick on someone their own size.