Is it possible to light a led bulb with AA battery?
Read about a circuit called "Joule-Thief".

Single AA battery cannot light up an led. An AA battery has a nominal voltage of 1.5V which varies from 1.1 to 1.5 depending upon how much the battery has been discharged. 

Most LEDs require 2.5 - 3.5V minimum to turn on. Reds LED turning on at the lower voltages while Blue LEDs require higher voltages. 

Two AA batteries in series can light up an LED since they together supply about 3V. This should work for most LEDs except Blue and may be White. More cells in Series will surely work but then you need to add a resistor in series to limit the current. 

There is one way with which you can use a single battery to light up an LED which is a Joule thief circuit. https://en.wikipedia.org/wiki/Joule_thief

It uses an oscillator to increase the voltage at the expense of a higher current draw.