On the 30-odd occasions I've played Bethpage as a single over the last 15 years, I've never made a reservation, I've never had a problem getting on, and I've never waited more than an hour to do so. My trick: Arrive around 2pm. This way you don't have to wake up early, you can check course status in the morning by calling the automated system that updates every day, and you can play at the best time of the day, the late afternoon/early evening.
Good luck, and enjoy!