Abstract: An improved sports accessory bag with straps which are convertible for use either with a bar on stationary exercise apparatus, or for use as a portable accessory bag. A strap is attached to one end of the bag and a second strap is attached to the opposite end of the bag. A first separable buckle is used with the first strap for forming a first suspension loop. A second separable buckle is used with the second strap for forming a second suspension loop. The first female snap receptacle and the second male snap connector are compatible for connecting the two long free ends of the two straps together, so that the first and second long free ends will form a third suspension loop. The bag may be suspended from the first and second loops on a bar member on stationary exercise apparatus, or it may be converted to a portable sports accessory bag by connecting the long ends together around a person's waist.