Those bumps happen because each square your mesh has its actually two triangles (Quad), and the texture deforms through the line that divides those two triangles. There are several ways of making this less noticeable, one of the most obvious one is actually adding more vertex.
Other way may be apply the mesh to a tail that is not bent over. If you apply that mesh over the straight tail when you bend it it will look a bit more square-y but a bit less deformed.
The best solution to this problem (for my taste) is actually not abusing of meshes for everything, and it's a problem of design. Work with this limitations and try to make designs that keep these graphical artifacts to the minimum.
I've been working with a friend on some libgdx test using meshes deformations aside from spine and this kind of artifacts were impossible to get rid of. It is basically the same thing that happened to old psx games in their textures.
You can find a clear example of this problem here http://xboxforums.create.msdn.com/forum ... 38416.aspx .I've been looking for another more clear and detailed example I found a long time ago, didn't find it though. I think there's no way of solving this yet (I may be wrong though).