I don't know of any shuttles from POP to S.D. You can go to POP and "charter" a private plane. I think one way was about U.S. $250. some 8 years ago... and that was one way. Not knowing IF and When you would be finished and having them sit around with a plane will add up fast plus longer/higher cab costs and arriving later... that means a lot more time and costs.
Take the bus. Cab to a hotel and relax for the afternoon and evening. Cab to imigration to arrive at 8 AM. If things go well, out at 10 am and into a cab back to the bus station.