I hand wash bibs with 'gentle' soap, mostly so I can really target the nastee bits, not so much to spare them from detergents.

I'd make more of a point of making sure they're in lingerie bag, rather than worrying about detergents.

I've never had any Assosseseses, but, from my experience, lycra loses it's elasticity/conformity, or will be damaged from saddle rub before harsh detergents will break the fabric down