Relay to Mains lightswitch
All mains electrical work should be performed by a fully qualified electrician.

Yes, this relay board will easily switch a light bulb.

A note on current: A single 100 Watt incandescent globe will only draw 0.83 Amps at 120V AC (0.416 Amps at 240V AC). The equation I used: I=P/V. You would start coming close to the maximum rating after 10 globes (although I advise staying well below the maximum).

You mention that your bedroom runs on 15 Amps, which I assume means that the mains runs through a 15 Amp circuit breaker (or fuse). This circuit breaker will trip if the total current to all devices after it exceeds 15 Amps.

A similar question was asked by Matthieu Napoli over on the Electrical Engineering Stack Exchange site. There are a number of high quality answers there that would be helpful for you. Worthiest to mention is Cybergibbons answer where he recommends using the PowerSwitch Tail as a very safe way of switching mains voltage. You don't need an electrician when using the PowerSwitch Tail providing the light you are controlling has the matching plugs.