Question

Why does electric bulb doesn't glow immediately when switch is on?

Answer 1

Considering this, light bulb here implies, incandescent lamp. (I suppose)

As we know, whenever current passes through conductor, there is always some heat loss, denoted by (I^2*R).

The filament inside the incandescent lamp is generally made up of tungsten material. The hot filament is protected from oxidation with a glass or quartz bulb that is filled with inert gas or evacuated. The light bulb is supplied with electric current by feed-through terminals or wires embedded in the glass. Most bulbs are used in a socket which provides mechanical support and electrical connections.

Hence when the thin filament carries current through it, it heats up to high temperatures to give light output.
It will take some time to heat up the filament of the bulb that is why it takes a little time to glow but this time is very small.