Yes, you can add tea tree essential oil to a bath, but it must be diluted first to ensure it disperses properly and avoids potential skin irritation. Essential oils do not mix with water; they will float on the surface, which can lead to concentrated contact with your skin.
The correct way is to dilute 2-4 drops of the tea tree oil into a tablespoon of a dispersing agent before adding it to the bath. Suitable dispersants include a tablespoon of a full-fat milk, a carrier oil (like sweet almond or jojoba), or an unscented bath gel base. Stir this mixture thoroughly into your running bath water. This method helps the oil blend throughout the water, creating a more even and gentle experience. As with any topical use, it's wise to avoid overuse and be cautious if you have very sensitive skin.