I'm sure they aren't called gym bags, but PE bags just doesn't sound right!
I made something like this last year for Zeke and this year Joe has real PE. As in I-Get-to-change-my clothes-for-this-class. Oh and his brothers told him that a 2 minute change is expected...no sitting around and thinking about it.
SO that required a bag for PE clothes.
Take an old t-shirt...or one that has stains at the neck in this case.
Cut off the sleeves and neck.
Fold the top down about an inch...using the zig-zag stitch, make a sleeve for the draw string.
you need two strings...the length is determined by how big you bag is.
Take the first string and thread it from the right side of the bag, the WHOLE way around until you come out the same hole again. Take the 2nd string and start on the left side of the bag again coming out the hole you started.
Take the two loose ends on the right and bring them down to the right bottom corner of the bag....make a pleat and stitch (with the sewing machine) the string ends into the pleat. Do the same on the left side of the bag. You can use it for a light weight back pack too.