You can do the burn test...find an ashtray or old bowl, cut a small piece of fabric, set light to it and let it burn. Look at the residue, if it has any stickiness it is a poly blend. Pure cotton burns fast and clean...no messy gunk.
Don't however do this in the shop!
Often the bolt ends have the type of fabric written on them, sometimes the selvedges. Generally though I would think the store-owner would be honest, otherwise they wouldn't get repeat business.