Is it bad luck or bad genes that made me develop bursitis?

Bad luck, etc.. Genetics rarely play a role in bursitis. Direct trauma, overuse, poor body mechanics and age-related degeneration are the most common factors associated with bursitis.
Neither / overuse. Bursitis is typically an overuse injury whether you do too much exercise and get bursitis in the shoulder or too much walking and get hip bursitis, it is basically overuse. It is typically treated with rest, ice and nsaids. Sometimes a local cortisone injection or physical therapy is necessary.