To reach Koyembedu(CMBT) from Sholinganallur, you can get in 570 AC Bus (Direct bus).

570 starts from Kelambakkam and goes via
Perungudi,
Toll Gate,
Velachery,
Olympia Park(Guindy),
Ashok Nagar,
Vadapalani,
CMBT.

Otherwise go to Velachery and catch D70 (frequent bus)