In reply to Donnie:
As noted above, it's almost certainly down to coordinating the various muscle chains.
Hamstrings should be strong, but it's your glutes that should be doing most of the work. For most people, most of the time (generalisation), problems come when they use quads or hamstrings to compensate for weakish glutes. The kind of bridging exercises you are talking about will only be effective if you are taking care not to do too much of the work with your lower back or hamstrings. It might be better to try hip thrusts, both double and single legged so as to isolate your glutes. Google for loads of videos and articles.
Another thing to consider, particularly if you notice a significant loss of control/power when you switch to one leg, is that big 'prime movers' like glutes and hamstrings depend on the stability of your hips and back to do their work. In rooves a huge amount of work is done using deep muscles around the pelvis and ribs to keep the trunk/hips/shoulders stable while you do the work. A combination of planks, side planks, bridges and levers will help to train these, or (better) lots of steep climbing on good holds.
Mark