Is there a bus from Kunming Railway Station to the Stone Forest for the round trip?

Yes, several long-distance buses run between the railway station and the scenic area.
To the scenic area, the 12 schedules are from 10:10 to 19:10.
About the return way, also 12 buses depart from 07:10 to 16:40.

Excellent, thank you. Is the 16:40 bus to the Railway Station the last trip anywhere into the city? Is there any other way into somewhere else in the city? Essentially I'm just wondering if I have to head back to the city at 16:40 or is there is a later option to get me into KM.

Well, as I know, except the 16:40 bus to the Railway Station, there are also several coaches that can take you to Kunming East Bus Station. But I cannot find the exact schedules.
You can consult the staff upon arriving at the scenic area. :-)