How to get to Chiayi from Tatajia with bus

Hi, me and a friend will be day hiking Yushan Mountain on May 31. W'll be staying in Dongpu Lodge on 30 and we'll start the hike at 3 am and we think will get down at around 3 pm. I would like to know if there are other bus that can go to Chiayi so we can ride a train to go to Taipei. I've read somewhere that the last bus that goes through Tatajia to Alishan will be at around 12 pm so we might miss that bus. Thank you.