Is it safe to put bactine on a new navel piercing?

Of course: Will help reduce infection risk--may sting just a wee bit, but builds character (?) ;) not a bad idea.

Body Piercing: Apply a cold pack to help reduce swelling or bruising. Never apply ice directly to the skin. This can cause tissue damage. Put a layer of fabric or a cloth towel between the cold pack and the skin. Wash the wound for 5 minutes, 3 or 4 times a day, with large amounts of warm water and an antibacterial soap, such as Phisohex or dial. Avoid tight clothing over the piercing area.