Hi there, Do you know if there is a bus that goes from Zhongshan Park or Changning Rd to the Jiaotong University area?

I think the local subway is much suitable for you.
From Zhongshan Park Station, you can take the subway line 2 to reach Jiangsu Road Station where you can change to line 11 to reach Jiaotong University Station. Get out of the station, you can see the university easily.
There is no direct bus between the two places, unless you want to take a taxi.