What are some hamstring stretches I can try as a biker?
I think that your biking may be a culprit in terms of your tight hamstrings, but I also think that the yoga you do is a wonderful way to elongate muscles that become contracted during other forms of physical activity. Thus the two forms of exercise can coexist happily.
I don't know what stretches you are doing, but I have a favorite hamstring opener. What I like about this stretch is that it is very simple, and it focuses directly on the hamstrings, unlike such poses as Adho Mukha Svanasana (Downward-Facing Dog) or Paschimottanasana (Seated Forward Bend), which also involve the lower back. This hamstrings-only quality is useful because we can then see the actual degree of tightness in the legs, without being misled by what is sometimes actually a lower back issue. This stretch can be done daily and, as long as you are conscientious about not forcing, it does not require a warm-up to be practiced safely.
Have a strap or some kind of belt handy. Lie on your back with your knees drawn into your chest. Keep your right knee drawn in, and place your left foot flat on the floor so that the leg is bent, knee pointing up to the ceiling. Place the strap around the ball of your right foot, holding the two sides of the strap with each of your hands. Slowly, without forcing or straining, start to extend your right leg toward the ceiling. Don't worry if it doesn't go straight; just keep gently pressing into your heel and drawing the ends of the strap toward yourself. Give yourself enough length on the strap so that it remains taut but your shoulders remain comfortably on the floor, rather than hunching up toward your foot. Do this stretch every evening for a couple of minutes on each side.
Over time, as you're able to bring your leg straighter, keep directing your energy into your heel. Eventually, if you can extend your leg straight up to the ceiling, the heel will be higher than the toes. Once this happens, continue to prioritize length over depth. In other words, don't sacrifice the length in the back of the leg in an effort to pull the leg closer toward yourself, although eventually you may be able to start pulling the leg in as a way of emphasizing the extension.
See also Enjoy the Ride: Yoga and Biking