Like another person said, I'd probably try to get there at least 10 minutes before the arrival time in San Bernardino. You probably could get away with 5 minutes before if you really hustled after you park to get to the train platform, but I prefer at least 10 minutes(if not 15) just to be safe. I know at certain busier Amtrak depots in the Midwest(Chicago, Milwaukee, and I think also Saint Louis), they lock up the gates 5 minutes before train departure.
The 45 minute recommendation you saw btw, is just for staffed stations IF you are utilizing the checked baggage service with your bags at the few stops that offer it. And of course, only a handful of stations handle checked baggage(i.e. LA, Fullerton, Flagstaff, Albuquerque, etc) on the Southwest Chief, and most don't offer checked baggage service. Which includes San Bernardino, where you're boarding.
Honestly, I'm someone who prefers to get to the station before the train arrives, preferring to have no less than a 5-10 minute cushion before the scheduled arrival time. But that's just me.