Would side bridging be good for the SIJ to prevent pain in gait?

Side bridging particularly strengthens the quadratus lumborum (QL) and tensor fascia latae (TFL) as the major mobiliser muscle groups. When you take weight through your leg you need a pelvis that can transfer the load from your leg to your trunk efficiently. In the stance phase of gait, therefore, your SIJ on the weight bearing side must be in a stable, "close pack" position (see the diagram below).  And when you swing your leg in the swing phase there needs to be some give in the pelvis to allow movement to occur, called the loose pack position in the SIJ. The close pack position for the SIJ is a posteriorly rotated ilium bone against a "nodded forward" or nutated sacrum.
The muscles that produce and control posterior rotation in the ilium are the oblique abdominals and gluteals, and multifidus nutates the sacrum. If these muscles are dominated by preferentially activated QL and TFL (+/- Iliocostalis and longissimus), the ilium is pulled into anterior rotation.  An anteriorly rotated ilium in the weight bearing phase of walking creates a loose pack joint which is much less efficient at transferring forces from the legs to the trunk, risking the development of pain and pathology. Low threshold activation of the gluteals, obliques and multifidus will facilitate the close pack stable position of the SIJ for walking, in addition to the local muscles for added functional joint stiffness. Tightness and over-activity in QL pulls the ilium anteriorly, and tightness/overactivity in the TFL can pull the ilium anteriorly in the hip extension phase of gait.
Therefore exercises other than the side bridge are recommended for patients with SIJ pain! Learn how to assess for a SIJ that fails to lock into a close pack position in weight bearing and what to do about it to prevent pain in the pelvis in walking in the Motor Control Retraining for the SacroIliac Joint workshop in Auckland and Wellington September 22-23, 2012.