The top of a handlebar bag used to attach to the handlebars, one attachment on each side of the bag. Not only would this provide lateral stability to the bag (which were quite heavy when on camping trips), this attachment method also prevented the bag from falling/sagging downward.

In picking a bag, be sure it can hold a full-sized notebook, a laptop maybe even a loose leaf binder. If any of those need to be carried and have to be put in the bag spanning the diagonal of the bag, it really limits the utility of the bag. If you cannot close the bag with those inside, it really limits the utility of the bag. If they don't fit at all, you have the wrong bag.