That depends on which genital piercing you have! Some heal in as little as 4-6 weeks, such as inner labia or VCH for women, or the Prince Albert for men. Others can take many months to heal.
Most bodies of water do harbor bacteria, including your bathtub (if you don't wash it with a 10% bleach solution first), and pools, Jacuzzis, lakes, rivers, and oceans. It is best to avoid submerging the pierced area in such bodies of water during healing.
Some body piercings lend themselves to being sealed with a waterproof bandage, but there are still some risks of water leaking in.
A piercing is an open wound, and you must avoid exposing it to germs throughout healing.
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That clearly is a question for the surgeon who performed the procedure. Anyone else giving you a casual answer has no way of knowing if there are special circumstances to take into consideration.