take a bottle of cold as you can get water in your handbag into the cubicle with you and run the cup under it to make it more springy/firm to help getting it to open up.

try the labia, origami or diamond/half diamond fold with one airhole in the fold that opens up first.

once inserted, press one side of the vaginal wall away from the cup for 10 seconds or so to create an air channel for air to get into the cup.

you can also try pressing sides of the cup that aren't open, turning or twisting the cup if you can (don't worry if you can't) or tugging on the stem. you can also try doing some kegels/squats/knee ups or bends or wiggly bum dance after insertion to get the cup into position.

make sure you're aiming the cup towards your cervix! it may be that you were missing it slightly, despite what most of the manufacturers instructions say you want the rim to be right underneath or around your cervix.

I have a Natural Mama and the half-diamond fold works pretty great at popping open. Make sure one of the holes is in the fold. I've tried it with the fold facing front and fold facing back and both seemed to work fine but you might find one way may work better for you.