Are there bullet trains from Taiyuan to Beijing International Airport?

No, there is no direct transportation between these two places.
You can take the bullet train from TY South Railway Station, get off at Beijing West Railway Station first. The duration is about 3 hours.
After arriving, take airport shuttle bus line 7 to airport directly. The buses depart from 05:10 to 21:00. And the ticket fare is CNY 24 per person. :-)