Can I protect my Bigfoot sighting?

No. However, you can copyright your photograph of Bigfoot. You can copyright original works of authorship fixed in a tangible medium. The Copyright Act contains the following works of authorship categories, the examples provided are not exhaustive: literary works (book, article, piece of writing), musical works (sheet music), dramatic works (plays, screenplays, scripts), pantomimes and choreographic works (arrangement of dance movements usually accompanied by music), pictorial, graphic, and sculptural works (paintings, photographs, maps, prints), motion pictures and other audiovisual works (film, videotape), sound recordings (songs on a CD, recording of musical works), and architectural works (blue prints). It does not protect ideas-patents protect ideas. It also does not protect names-trademarks protect names.