I have two
how are you trying to give your budgie a bath? you can get those little baths that you can stick right on the floor of the cage, or hang off the door of the cage. but you may have to leave the bath in with the parakeet for a while, sometimes it takes awhile for them to warm up to the idea of actually getting wet lol.
my birds are polar opposites of eachother. As soon as I put the bath in, Joey jumps in immediately, and if I'm using the bath with the mirror on the bottom, he'll finish his bath quickly and just spend the rest of the time sitting on the side of the little tub talking to the bird in the mirror.
Angel on the other hand has to sit back and watch Joey play in the water first before deciding that its probably safe for him
but typically you'll find that budgies generally don't like to be outside of their cages, because well their cage is there home heh. You have to train them slowly to get used to being out side of the cage, just spend a few minutes each day playing with your parakeet outside of the cage, and he should get used to it pretty quick; just make sure there are no other animals around when you let him out, or any way for him to fly outside of the house.
pgp gave some excellent advice for caring for parakeets. a couple of other things to keep in mind are make sure you're not burning any candles around them, some parakeets are fine around candles, but for many they can be toxic, and be sure to keep your bird away from any drafts, as they can be quite dangerous for the little guys health too.
okay thats it, I'm done rambling lol.