The journey is rather tiresome considering there’s no direct bus straight to Sigiriya.
If you’re taking route from Pettah (Colombo), hop on either a No. 15 bus to Anuradhapura, No. 48 bus to Kaduruwela (Polonnaruwa) or a No. 49 bus to Trinco and get off from Dambulla (Rs. 190, Normal) or Habarana (Rs. 210, Normal). These buses run throughout the day, so you wouldn't have a problem finding one.
Take a Sigiriya bus from Dambulla or Habarana
Otherwise you can take a tuk tuk from "Inamaluwa" town which is located between Habarana and Dambulla