Mysore to Cochin (Ernakulam city) distance is about 400km.
Mysore to Cochin By Bus:
The most popular travel option between Mysore and Cochin is bus. KSRTC (both Kerala & Karnataka road transport corporations) operate many daily services between Mysore City and Ernakulam City. It's about 10-11 hours journey, most of the schedules depart around the evening and reaches Ernakulam/Mysore early morning.
Buses operate from the KSRTC bus stand in Mysore city. Though both Kerala & Karnataka RTCs operate luxury services, Karnataka's Club Class (about Rs750, one way) and the Airavat (about Rs700, one way) services are a shade better than the former.
These buses leave Mysore bus stand between 5pm and 6.30pm (4 services). Check ksrtc.in for schedules.
Most of them take the Mysore -> Gundlupet -> Sultan Battery (Wayanad) -> Kozhikode -> Edapal ->Trissur -> Ernakulam route. The Mysore to Wayanad stretch is about 3 hours and Sultan Battery to Ernakulam is about 8 hours.
One of the services goes via Gudalur and Nilambur. This is a shorter route.
Mysore to Cochin By Train:
There are no direct trains from Cochin to Mysore. One possibility is to travel to Bangalore and travel onward from Bangalore to Mysore. The train option is a bit longest compared to the bus option.
Mysore to Cochin By Road:
There are a few road routes from Mysore to Cochin. The shortest shown on the Google map many not be the smartest option. For driving from Mysore to Cochin, see Mysore to Cochin by Road.