Do I have to keep re wrapping my tattoo after I cleaned it?

No. Wrapping a tattoo up again causes a perfect place for infection to start.
Just keep it clean and moisturized.
If your artist didn't go over this, they are not a person worth returning to.

You should be leaving it unwrapped as much as possible. Tattoos need air to heal also you could cause an infection if you leave it wrapped up for long periods of time.

What saith your tatoo artist?

If no blood at all. No open holes or wound, you can let it go. Not recommend getting it more. It affect you luck, life and you.