It was very hard to find a satisfactory answer of how to get from Latacunga to Cuenca by bus. Online, there was a consistent story of getting driven out to the traffic circle on the Pan American highway and catching a bus from there.

We ended up taking a bus with Cooperatives Transportes Santa and it was much simpler. Their office is located close to the main bus station, you can see it here on google maps or here on open street maps. They’re open from 7:30 AM to 10:00 PM daily. 

We went there on a Friday and they told us the bus to Latacunga departs at 8:30 PM, 10 PM and 12:15 AM. We opted for the 12:15 AM bus so that we wouldn’t arrive in Latacunga in the middle of the night.

At 11:45PM we got a cab from our hostel to the bus station, it was $1.50 and we didn’t want to walk through town in the middle of the night with our giant packs. When we got to the bus station it had a waiting room upstairs where we waited until 12:15. At 12:15 a station employee told everyone the bus from Latacunga was here and it was standing just outside the office. We got on and were on our way. 

Hope this helps someone. If you have more/better information please post in the comments.