Molly,
If your mum does'nt give you anything more than the 50p a day to get you home from school, she really needs to be told what the implications are if anything was to happen to you, in an emergency and you need money you have'nt got.......tell her, for crying out loud..............I have two older children in High School....they both walk too and from there.......but i make sure they have a £5 note in their pocket, just in case of an emergency arising.
If your mum does'nt give you the money, which is unbelievable, and you can access money from your account, then i would take about £10 out....go to a shop for change, and take a litle extra each day with you, so you are not short, if anything happens.