as per your question, the aim is driving 230V ac bulb, using two 1.5V batteries. actually using two 1.5V batteries we can't drive a relay, so in first step, boost the voltage (amplify DC 3V to 5V or above 5V) then by using relay control circuit you can switch ac bulb.
2*1.5 >> Booster >> relay control circuit(with microcontroller or without microcontroller) >> connct AC bulb to relay.
note: takecare about AC connection when connecting bulb to relay.