I play tennis a lot; can it cause bursitis?

Depends. The two most common causes for bursitis are trauma and activity (with infection being a distant third). Bursitis can occur in the shoulders, elbows, hips, knees, and heels, with the elbows being the most common. Although "a lot of tennis" can increase you chances of bursitis, the risk is still small, yet the benefits from the tennis are great. I suggest one keeps up with the tennis!