I had parakeets for many, many years and had never seen any of them bathe - but I always put in a bathtub in the bottom of the cage and then left it there for a week. It would get dirty. So undoubtedly they did use it the first day and I just didn't see, and then they didn't use it at all after then because it was dirty.
With my current 3 parakeets, I now put the bathtubs up on top of their cage and fill them with fresh, warm water when I let them out. Often they'll go straight for the baths and splash around quite happily before settling down to preening.