A tanning bed should not be used until a new tattoo is completely healed, which takes roughly three months. Once healing is complete, it's still a good idea to take precautions to protect the tattoo and the skin.
The same ultraviolet rays that tan the skin will gradually fade the ink in the tattoo. The UV rays in tanning beds are more concentrated than those outdoors, so exposure should be limited. A sunblock with a high SPF is recommended before tanning, but it's not a good idea to use sunblock on a new tattoo until it has finished peeling and a new layer of protective skin has grown.