1.) To quickly bathe or shower, following the example of a bird, hence the name. Does not involve soap or shampoo, simply water. Typically done after strenuous activity causes one to sweat, and thusly, stink.
2.) To wash one's penis in a sink, in the situation that one might 'get lucky' that night and is worried that their penis may have a strange or unpleasant odor. So called because of the reference to bird meaning genitalia.
2.)OH shit, this chick said YES to go back to my place. I'd better go to the restroom and have a birdbath.