No matter what you use, eventually it will leach down into the water table or flow downhill to whatever or whoever is below you. I would use roundup (glyphosate) and try to keep it on the foliage, not on the soil. If you have a constant, every year weed problem in that area, you may have a re-seed problem - get those weeds early in the season or use a pre-emergent. I would never use bleach, its even more harmful to the environment than glyphosate.
Whatever you decide to do, wear your protective clothing and don't breathe.
