A large amount of gray water will poison the bean's soil. The detergent will hurt the roots' ability to absorb water and block up niches in the soil that would otherwise be used to soak up nutrients and water. This will eventually choke out the bean plant, killing it.
Detergents are designed to be corrosive toward organic materials and are no exception when it comes to bean plants. The detergent will strip away at the bean's waxy coating, making it difficult for the bean to reach maturity. The excess salt in detergents will also increase and alter the water's pH, which will prove detrimental to the bean's growth.
If detergent is used in very small doses, it can actually be beneficial. Small amounts of the detergent will kill and repel various plant-eating insects like mites, which in the long run will help the plant grow larger. However, it's impossible to know how much detergent is too much for the given plant, so this approach is not recommended.