Everyone's definition of "birdbath" varies.
Mine means a full shampoo in the bathroom sink.
Then move to a large stall with a lightly-soaped damp washcloth for a shoulders-to-toes scrubdown.
Follow it with a clean washcloth dipped into a very small bucket of clean water to wipe off the soap. Wring excess water into the commode.
Finish with a brisk towel-off. Then apply toiletries/dress.
I am very careful to keep the facilities very clean and I will wipe up any splashes with paper towels.
When finished, nobody can tell that the restroom was used; and I am just as clean as if I had taken a shower.