Why bulb glows immediately since drift speed of electrons is 10-4 m/s
Glowing of bulb is the heating effect of the electric current.
The electrons in a conductor start moving with drift velocity when an electric field is applied.
Current is not just one electron flowing from one end of a conductor to another. It is the overall flow of electrons throughout the conductor.
When an electric field is applied, electrons at all parts of the conductor start drifting. The electrons just near the negative terminal of the battery drifts, the electrons at the middle of the conductor drifts and the electrons near the positive end of the conductor also drifts. So, even if the drift velocity is the order of few cm/s, the current flows at the velocity of the propagation of the electric field, which is the velocity of light.
This is why, when you switch ON the bulb, we observe that the bulb glows instantly.