This happens more often than you think. :)
When booking your reservation, try to find a flight arriving / departing around the same time you need the shuttle. Use this information in your booking request. Also, please include these details and why in the "special instructions" area so the shuttle provide understands your special circumstances.
Once the reservation is booked, you will receive an email confirmation with contact information for your shuttle provider.
A few days prior to your traveling, contact them directly to remind them of your special circumstances!