Riding a bike is repetitious. Even a mild activity such as typing can lead to stiffness when done continuously. My guess is that your position on the bike is not the best. It could be you need someone experienced to help with fitting the bike, such as someone at a bike shop. Then again, you may just need to learn how to sit and be relaxed on the bike. One observation I would offer is that experienced athletes, whatever the sport, always look calm, relaxed and unhurried.

If you watch videos of pro cyclists, you will see that even during hard efforts, they are very smooth. There are many videos on YouTube showing the fitting process and instructions on setting seat height and position of the saddle and distance to the handlebar. Even when you find the perfect position and ride longer distances, the best position will change as your body adapts. So the best position is a moving target that over several seasons will change. Good luck and find that relaxed position.