Brad's Iyengar Yoga Notebook
Bharadvajasana is a seated twist that is asymmetrical in the legs, pelvis, and spine causing your rear buttock to tend to come off the floor (or blanket).   Though the nature of the pose is asymmetrical, you should still try to minimize the asymmetry in your practice of it.   It is helpful to practice this asana while sitting on the end of a bolster, both when first learning the pose, and even when you are mature in it as the added height helps to minimize the asymmetrical tilt in your pelvis.   An alternative support is to use a blanket under the buttock on the side that you are twisting toward (under the right buttock if twisting to the right).
In all twisting asanas, perform the twisting toward the right side first since these poses squeeze the colon and you want the compression to move from your right side toward your left side to facilitate the natural flow of digestion.
As in all twists, the twisting action of Bharadvajasana begins in your pelvis, from your pubic bone, and moves upward.
As you begin the twist (and throughout the pose), lift your chest toward the ceiling.   Lift from the top of your sternum to lengthen the front of your torso as much as possible.   A long spine is crucial to a good twist.   If you are twisting to the right, press your right shin into floor to help you lift your torso.   You can extend your right hand back and place it on the bolster or floor, using it to lift your spine straight up perpendicular to the floor.   When you no longer feel you need this assistance, you will reach around your back with your right hand and grasp your left arm.   This action will also aid in expanding your chest and lifting your torso with a different kind of leverage than that of pressing down on the bolster or floor.
Use your left hand on your thigh to pull your torso to aid in the twisting action.   On each inhalation, lift your spine with your right hand on the bolster or floor.   Be as tall as you can be in every twist you perform.   On each exhalation, twist your spine slightly more to the right with your left hand.
As you twist to the right, try to keep your left sitting bone as close to floor (or as close to resting on the bolster) as possible.   Try to drop both your sitting bones to the floor or support as equally as you can.
This asana creates a slight backbend in your upper torso.   Pull your shoulders back and downward.   Draw your inner shoulder blades deep into your back to help you lift your chest upward.   Avoid the natural tendency in all twists to raise the shoulder that is twisting back.
Allow your head to follow along in the direction your torso is twisting.   Do not lead the twist with your head since this can place too much tension in your neck.   Turn your head as a natural action of spiraling your spine, not as its own independent action.
A wall is a useful tool when practicing twists.   For Bharadvajasana, sit at the wall with your legs on your left side, the wall on your right, and both of your hands on the wall helping you achieve lift in your torso and "assisting the twisting" toward the right.
Repeat all of these actions in the pose on the left side.