Recently my budgie has been losing a lot of feathers lately and he is looking a little scruffy. We've been feeding him lettuce and bird seed and we've been trying to get him on some other foods but he's been unresponsive to them.
You can't see it in pictures (that's why I'm not posting one), but he has little black bits on his forehead too. Maybe I should try to give him a bath?
No, you should never forcibly bathe a budgie.
You can offer him a shallow dish of water to see if he chooses to bathe in it.
If he likes being lightly misted, you may do that.
Be sure to aim the mister into the air above him so the droplets fall down on him.
Don't squirt water directly on him.
It sounds as though your little budgie is simply molting which is quite normal.
The black specks you see on his head are pin-feathers.
It is important to work to get your budgie on a healthier diet.
Does he like egg food? The protein in the egg will help him through the molt.
As FaeryBee has said, absolutely do not force your budgie to have a bath or handle him when his pin feathers are coming out. They are extremely sensitive at this time so you will want to minimize handling.
You can offer him, as FaeryBee suggested, a shallow bowl, or go to a dollar store (or another store) and purchase a small spray bottle that has a spray nozzle restrictor so it mists as opposed to a stream spray. He will have to get used to you misting him at first but if he doesn't like it that much then let him decide if he wants to bathe. Another alternative -- offer him some dill in a bunch, wet it real good and see if he bathes and eats at the same time.
Either way, you cannot force your budgie to like bath time but you can offer him ways to enjoy and learn on his own.
Bless him, he's moulting
Think back to when you were a child and you were losing your baby teeth....they were wobbly forever and a real pest.Then to add insult to injury the grown up teeth started pushing through, and they hurt.
That's the best example I can think of to explain to you how your budgie feels....things are happening that are supposed to happen but it doesn't stop you feeling out of sorts and grumpy.
And yes, he will look a mess whilst all this is going on....and those little pinnies must itch like crazy
I know people who keep all the feathers and stitch them into tiny cushions!