The more hats that you wear in Hollywood the better off you are. There's even a term for it: "hyphenate." There are zillions of actors and writers in Hollywood. If you can write and act, crafting a one-person show may be the way to get noticed. In the 1980s, actor Chazz Palminteri's career was barely scraping by with tiny bit roles and nightclub bouncer gigs. He was just about to pack it up, when he decided to enroll in a theater workshop run by Mark Travis, a teacher with prior experience producing one-person shows. In the workshop, Palminteri told a true story about witnessing a murder in front of his house at age nine. From this story came a monologue that spawned more stories that eventually became his one-person play "A Bronx Tale", which became a movie starring Robert DeNiro and Palminteri.
From a theater producer's viewpoint, a one-person show's main advantage is budgetary: one actor/writer. From the performer's viewpoint, a one-person show is an extended audition without competition from other actors. It's a screenplay performed live before Hollywood industry types who don't know how to read and would prefer not to read a submission.
Ask yourself how committed you really are to writing and acting as a career. This is a serious question, because you need very thick elephant skin for the theater or motion picture business.
Find an acting or playwriting workshop where you'll be given the creative space to find a personal story or a character that resonates strongly within you.
Many successful one-person shows have emerged as almost a form of therapy in workshops and/or collaborations with teachers. Since this type of writing is also a performance, keep an audio or video recorder on hand.
Write it all down as if it was a novel or a comedian's monologue, and keep revising. For formatting, pick up copies of successful one-person shows such as William Luce's "Belle of Amherst" and any of the late Spalding Gray's works.