What is the best way (except taxi) to travel from PEK to Zhuozhou (Hebei)?

There is no direct bus to Zhuozhou from PEK. You may take shuttle bus line 10 to South Railway Station. Then, take a bus to Zhuozhou from the nearby Yongdingmen Bus Station. The buses are available from 5:00 to 19:30 at intervals of 30 minutes. The trip takes about 2 hours. The fare is CNY 24.
Or, you can take shuttle bus line 7 from PEK to West Railway Station. Then, take a bullet train to Zhuozhou (25 minutes).

You can choose the way you like. :)

Thanks a lot, Angela! I thought about the West Railway Station. A bus to Zhuozhou is a "plan B" ;)

That’s also available, and you can take the bullet train from West Railway Station to Zhuozhou. The train takes about 30 minutes and CNY28.5 for a second class seat, CNY45.5 for a first one.
By the way, you need to take Shuttle Bus line 7 to West Station.