EVERYDAY !
 
a duck without water is an abused duck.
 
They need to swim and be able to splash around. Thats how they clean themselves and it helps spread the oil. A bath will also rinse off any poo thats stuck to feathers although thats minimal.
 
Has the ducks leg been set and stabilized? I keep hearing ":lame" and recall you saying it was broken,  but has anyone actually set the leg or given the bird medical attention?  Because its possible if the leg is badly damaged that the duck could loose it...tissue dies, it cannot heal and regrow the bone, and it has to be taken off. Thats not really possible on a duck. I'm hoping that the leg has been set and treated somehow, so its at least stable so it has a chance of healing. Otherwise the poor duck will be un-necessarily crippled if it is able to survive the injury without treatment. Ducks are resiliant but broken bones DO need to be set and aided,. they walk on them and they don;t have a magic wand to heal broken bones. We know to not put weight on a bad leg, a duck has NO choice. It will try to walk when its dying. They can;t say "it hurts" or "please help me"..
 
Baths are good for exercise, cleanliness and health. Don;t freak out over duck poo in the bath water. it happens almost instantly. They let it go when they are nervous and as they relax. Just give her a good rinse when you're ready to take her out and she'll be fresh as a daisey. A shower massage is a good thing to have when a duck lives in your tub.
If you give her a hour in the tub each day she'll be a much happier duck and have better health.
There are no big secrets to good duck health...feed them greens with the bagged food, let them swim, always have clean water for drinking. Lots of attention and affection and your duck can live for many many yrs. I've heard fo 20 yr old ducks before. Many that are 10+.
I hope that your ducks leg is stable and healing...I hate to think of an animal suffering....I know too well what its like to walk around with broken bones. It hurts.