Is the fitting on the bag a female side release buckle? (E.g.:
If so, there will (almost certainly) be very tiny lettering on it (possibly inside it) identifying the manufacturer and model. It might be ITW Nexus, or Hi Tex, or any of quite a few manufacturers. (Each side release buckle is slightly different, so you probably need the exact mating part.)
Given the manufacturer name and rough dimensions, you can probably find the mating part and get a shoe repair shop to make you a strap.