Calcultions to choose between a transistor (switch)
You're best bet is to use the following:  Connect your bulb to your 12 volt source in series with your resistor, which is in series with your transistor (Collector side on an NPN BJT).  Then connect an arduino pin, in series with a resistor, to the base junction.  Finally, connect your Emitter to ground.  The problem with your calculation is that it assumes all of your voltage is being dropped across your bulb.  You can't do this, because you'd need current to flow through the circuit, which means you'll need to add a resistor, which will take a voltage drop of its own (V=IR).  Your best bet is to find the right balance between the voltage drop that you need across your bulb, and across your resistor.  As an example, if you drop 10 Volts across the bulb, this means to generate 5W, you'll need to limit your current to 500mA (P = IV).  This leaves 2 Volts that can be dropped across the resistor, giving you a 4 Ohm resistor.  Also keep in mind: the resistor you choose will need to be power rated appropriately (in the example I used, it needs to be rated for 1 W), and you'll want to make sure that the transistor can handle the appropriate power dissipation.  For most BJTs with a high enough Beta value, your Emitter and Collector currents should be equal, so I wouldn't worry too much about any voltage drop across the transistor.  I hope this helps.