While it's fairly safe to say that my core is pretty strong, even when I am performing the most basic variation of this exercise, I am still able to feel the muscles in my anterior core and obliques working to prevent my body from resisting extension and rotation.
Like most exercises, there comes a point where in order to keep improving, you need to to make the exercise more difficult. Here is a more challenging variation of the bird dog. I used band resistance to increase the difficulty of the exercise. If you are performing the exercise properly, it is actually quite tough!
Some key points:
1) Attach the band around your foot and grab with your hand of the opposite side. Obviously the thicker the band, the more challenging the exercise will be. Or, you can adjust the resistance by holding higher or lower up the band.
2) Before you extend your arm and opposite leg, actively exhale and tuck your rib cage towards your pelvis. Keep your leg and arm relatively relaxed as this will force the muscles of the anterior core to work harder to resist rotation and extension.
3) Pay attention to your alignment. Your body should be in a straight line from your head to heels. Do not let your neck collapse, back to hyperextend, or your torso or pelvis to rotate.
4) Extend your leg and arm so they are roughly parallel to the ground. I could have lifted my arm a little higher, but my main focus is on the above three points.
5) Do not shrug your shoulder as you lift up your arm.
6) Feel the movement, don't just move! Mindlessly going the motions will achieve nothing.