I did not learn the recipe for the Beanbooster circuit after Jimmy scanned the Bee Queen. It should be noted that I scanned her in the beginning of the fight, and retrieved Jimmy after the fight was over. It took about maybe 10 minutes or more.
1. Hammer Bee Queen hive.
2. Use Pan Flute to make her sleep.
3. Make Jimmy scan her.
4. Defeat the Bee Queen. For me it took about 10 minutes or more. The time here may be important.
5. Retrieve Jimmy.