Consider adapting a Dopp kit.
I've never tried one but someone online had dopp kit's with added straps to hang on a saddle.
Can find a wide assortment of them in canvas / leather, faux trim, etc. I've seen nicely styled designed with offset zippers, the distress style, some already having extra loops where one could easily add small straps, waterproof type (but may leak thru the zipper). Target has some nice vintage looking Dopp's for under $15.