GCSE or A level? Do you want a mainly workshop based outcome or happy to go the textiles route?
Personally I’d avoid anything too small, fiddly and engineering based. You probably don’t have the kit at school (have you guessed my day job yet?) that can work with the sort of tolerances to do a job as well as the existing products you will inevitably have to do some product analysis against. You will ultimately be disappointed by the quality of the outcome. I would go down the line of accessories or cycle related issues.
[*]There are some great “smart” electrically conductive fabrics you could play with and look at additional lighting built into commuting clothing.
You could look at developing a first aid kit that packed away but unpacked and worked in an interesting graphical way to help an inexperienced first aider work out what to do.
Packing away, storing, transporting of bikes themes are always popular. Can you think of a new angle though?
A lad I worked with lashed up set up to take film of himself from a zip wire in the trees above his local run (look at my post history and look in the self filmed thread to see what I mean). A commercialised kit to convert a smart phone into a ariel film device could be fun.
Go left field – the problem might be the wasteful disposal of cycling components. You could design a product that reuses (upcycles) components in a new and unusual way. A bike rack made out of the rear triangles of bikes destined for the skip for example[/*]