You'll probably need to get that info from the Korat bus station, the new one just past the Terminal mall.
Last bus from Korat to Phimai leaves around 5:30 PM. (changes daily)
Last bus from Phimai to Korat leaves around 11:30 AM.
If relying on bus service and want to visit the historical park, you'd plan on an overnight stay.
There are (I think) 3 bus services from Mochit Station to Korat, all same price about 256 baht.
Nakonchai Air is comfortable, has wifi.
Korat Pattaya also comfortable, no wifi.
Chudchai.......seats too cramped.