Bus timings from Kumily:

Thekkady: 0930, 1045, 1130, 1200, 1230, 1330, 1530 hrs
Kumarakom: 0700 hrs
Munnar: 0600, 0945, 1330 hrs
Ernakulam: 0700, 1330, 1515, 1630,1715, 1930 hrs
Thiruvananthapuram (from Kumily): 0840, 1530, 1615 hrs; (from Thekkady): 0820, 1515 hrs
Kottayam: Frequent buses
Alappuzha:1115 hrs
Cherthala: 1415 hrs
Idukki:Frequent buses
Chennai: 1630, 1900 hrs
Pondicherry: 1630 hrs
Madurai: 0115, 0515, 0525, 0645, 0716, 0720, 0730, 0755, 0835, 0940, 1030, 1045, 1120, 1155, 1300, 1315, 1320, 1420, 1515, 1540, 1550, 1650, 1705, 1800, 1840, 1905, 2045 hrs
?Dindigal: Frequent buses
Kodaikanal: There is no direct bus from Kumily to Kodaikanal. The Dindigal bus takes you to Vathalakundu from where there are frequent buses to Kodaikanal (149 km)
Trichy: 0855, 1045, 1925 hrs Palani: 0930, 1135, 1830, 1850 hrs