How to switch on an AC bulb using arduino as well as regular switch?
This can be done (to a certain extent) using a SPDT (Single-Pole-Double-Throw) relay and an SPDT switch.

The basic principle is the same as when you have two light switches controlling the same light (such as on a staircase - one switch at the top and one at the bottom).  The two switches alternate between one of two different paths for the current. When both switches are routed to the same path the light is on.



Both the Arduino and the switch can turn the light on and off at will. The only problem, though, is that the Arduino has no clue if the light is on or off. To know if the light is on you will need some kind of feedback mechanism.  That might be a simple LDR that looks to see if it's light or dark, or some kind of current monitoring system (current transformer, hall effect current monitor, etc) which the Arduino can use to see if current is actually flowing through the lamp circuit or not.