The only thing I can think of is they don't have any buses going that early (which is hard to imagine) or your flight is earlier than their suggested 12:30. What's the point of sending you a letter while you're on the ship

Just a suggestion: go straight to the SuperShuttle/Prime Time shuttle staging area--it's right outside the terminal. Just tell them you want to go to LAX; that's where 90% of them are going anyway; you don't need a reservation.