A bulb has resistance R, the current in it is given by V / R, where V is the voltage difference between its ends.
when two bulbs are connected to a mains in parallel, then V is same for both. So current is each is V / R.
when the two bulbs are connected in series, the resistance in the circuit is 2R.
So the current through the resistances are = V/2R.
So current is more when they are in parallel with the mains.