OK - I tried hard to find an image or video of the hip flexor strengthening exercise that I wanted to share with you but alas, I could not find one.

So I will try to describe it. Stand at a counter top or table, lean forwards using your hands for support until your body is in about the same forwad angle that you would have in your most typical riding position on the bike. Reach the weak leg out behind you (as if you were pushing something away from behind) then bring you knee into your chest as far as you can. Hold it until you get the burn and repeat for 1 to 2 minutes. When you're good at that and It doesn't really feel like a challenge then you can go to moving in and out of position quickly for 3 sets of 40. When that's easy, you can add an ankle weight or elastic band/tubing for resistance. You don't get to go to the next phase until you can do the previous one well and without symptoms.

You can also do one legged drills on the bike. Those help. The important thing in either exercise is that the movement is coming from the hip and not from the low back or pelvis, these should be stable.