You can take bikes on all NJT trains during off-peak hours, and you'll be fine in the station, too. Hug the right side of the stairs when you're hucking the bike, and don't smack anyone in the face with your rear wheel; you won't be any different from the scores of slow pokes with heavy suitcases. I've never gotten any flak unless I bring my bike during peak hours or holidays (by mistake).
Penn Station at 1am is safe, if sometimes eerily empty and full of sleeping homeless folk and drunk B&T-ers. There's still ample police presence, and guards, too, usually.