Just been looking into it myself. Think you just pay when you get there.
At The Festival and The Open a shuttle bus service will be operating, picking up at Cheltenham Spa Railway Station and outside WH Smith in the centre of town before dropping off at the Racecourse. Return buses pick up from the Racecourse with stops at Pittville Street and then the Station.
• Return from Station - £5
• Single from Station - £3
• Single from Town - £2.50
• Single from Racecourse - £2.50
Read more at http://cheltenham.thejockeyclub.co.uk/plan-your-race-day/vis itor-information/directions-parking#44erRXMwDfJjFRoZ.99