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.
1.) OH shit I just shoveled 18 inches of snow and forgot deodorant. I'd best go and have a birdbath.
2.)OH shit, this chick said YES to go back to my place. I'd better go to the restroom and have a birdbath.