Due to contrary belief, Budgies do need baths. There are six  ways to bath your budgie:
1) Shower:
This way should only be attempted when your relation ship with your bird is very deep and they are tame. Take your bird with you to the shower and you can put them either on a specially made shower perch (picture below), or have them sit on your shoulder, arm or shower curtain. Then put the water on at a low speed so no powerful sprays, and make sure the water is warm. Don't have the bird right in front of the direct spray for it could injure your bird. If you're bird does not like this then don't persist with it.

2) Dish:
You take a shallow dish or bowl and put about 2-3 inches of warm water in and put it in your bird's cage and let them have some splashing fun. You should probably supervise this if you can to make sure there's no danger. Also you could put some greens ( lettuce, parsley etc) in the shallow dish for budgies usually bath in greens in the wild.
Tip: It may help the shy birds if you bring up the dish to them so they could see that it poses no harm.
Also my bird will only bath this way if the dish has a mirror in it you can also put toys to entice them

                          

3)Bird Bath:
You can buy bird baths that attach to the inside or outside of your bird's cage. Hanging a little treat in or beside the bath may entice them to it.

4)Plant Mister:
You can use a plant mister that HASN'T had any chemicals or pesticides in it. Put warm water in it and spray them from a distance on their backs not on their sides or in front of them. If they enjoy it, they will spread their wings and even chirp a little.

5)Sink:
Again this way should only be used if your bird is very close to you. Take them to a sink then put them on your finger or arm  and slowly bring them to the water. Not a lot of budgies like this way so you never know. Don't freak them out, any sign of fear, stop with the faucet way. You can even make a puddle of water in your hands as well.

While bathing your budgie, consider the following:
The location of the bathing is free of any drafts or breezes.
You should do it in the morning so your budgie has time to dry off.
If they are soaked, then you can blow dry them at a far away distance, on LOW speed and making sure the hairdryer has NO Teflon for that could kill your bird.
Make sure the water is always warm.

If your birds don't like bathing, don't force it, just keep trying.