Playing bonus games is great way to level up your tier.  You can even auto-play innings in bonus games! 

Access bonus games either from the Games button at the bottom of your main screen, then scroll right under "Your Turn"

or from Compete button at the bottom of your main screen.

Bonus game tickets are fairly easy to come by - they may be awarded for completing one or two levels of an event such as Walk Off Hero,  completing challenges, or you may purchase them directly in the Store by tapping on Boosts.