So when you start a game, is the #1 star relay energized?

Can you post a pic of the no. 1 star relay with its wire connections?

I thought maybe some wires were crossed, but they look fine.

Hmm. You may need to do some experiments. Whether you get a single or double bonus is determined by two make/break switches on the No. 1 Star relay:
Grand Prix Bonus count (resized).jpg
As drawn the circuit awards a single bonus. The make/break switch in the upper red box lets one pulse per score motor cycle (180 degree score motor rotation) from the Motor 5A switch get to the appropriate Bonus Reset stepper coil. At the same time the make/break switch in the lower red box lets five pulses from the Motor Imp-A switch get to the 1000 Point relay. So every score motor cycle the 1000 Point relay fires 5 times and then the Bonus Unit steps down once, or 5000 points score per score motor cycle until all the bonus is counted.

For a double bonus the No. 1 Star relay fires which flips the two make/break switches in the red boxes. In this scenario the upper switch lets 5 pulses per motor cycle from the Motor Imp-C switch step down one of the Bonus steppers five steps. The lower make/break switch sends five pulses from the Motor Imp-A switch to the 10,000 Point relay. So every score motor cycle the 10,000 Point relay fires 5 times and the Bonus Unit steps down 5 times, or 50,000 points score per score motor cycle until all the bonus is counted.

See if your bonus counts behave as described. Verify that the wiring of the make/break switches matches the wiring from the manual above. Try manually awarding a bonus while you watch the No. 1 Star relay and the two make/break switches. These might offer clues to what is going wrong.

/Mark