I'll say this: don't mess with anyone willing to tattoo a bear.
The SRD says...
How that interacts with a tattoo is anybody's guess. If I were running the game, I would be tempted to have the tattoo become non-functional in the original form, and functional in bear (and only bear) form.
I see it that the skin changes, not that it gets traded / replaced.
Therefore, what happens to tattoos is ambiguous.
Okay, you can see it that way. Human and bear skin isn't too far apart.
Then you have scaled creatures, creatures far too small to be a compacted version of yourself without having a specific localized gravity, colossal creatures far too large to be contained within a "changed" skin.
At some point, you create and destroy parts of yourself at a cellular level.