I will be arriving at Guiyang North Train Station and want to catch a bus to Chishui the same day.

Upon arrival, you can take bus line 266 from North Railway Station to Jinyang Bus Station. There are several direct buses to Chishui. The schedules are 9:00, 11:00, and 16:00, and the fare is CNY 168 per person.
Hopefully, you can catch the one at 16:00. You needn't make a transfer at Zunyi. :)

Thank you for the answer :)