Stretches keep me able to do even my most fundamental daily movements, including cycling and racing dirt bikes. We were taught stretches in football and track during high school. The Marines had us stretching before and during P.T. when I had my back injury and following surgeries stretches the physical therapist taught me and worked with me on perfecting have helped tremendously.
I'd say a good yoga or even water aerobics program to loosen muscles and strengthen joints would allow more freedom of leg movement for your mounts and dismounts as well as your riding in general.
Bill