Bike fit / correct riding position

I am predominately a runner, but I do still ride from time to time. I'm actually hoping to increase my mileage, but I find that after 10-15 mins of hard effort the hamstring in my right leg hurts a lot.

Does it sound like running has caused an imbalance in the muscles in my legs/lower back/glutes?

Is it a case of trying some shallow squats to help my Glutes?

Hard to say, you may have a twist at your pelvis, overly tight right hand side (esp if you are right handed), scoliosis in your spine. There could be the after effects of an old injury, a genetic weakness etc etc

Rather than diagnose the problem, it might be easier to find stretches and strengthening exercises that offer a solution.