Not your ordinary hard water deposit
Toilet bowls are made of ceramics which can contain feldspar. Toilet bowls also often have a feldspar glaze. There is a study that disolved Cr(VI) can be removed by feldspar.

Studies on the removal of Cr(VI) from waste-water by feldspar
http://onlinelibrary.wiley.com/doi/10.1002/jctb.280530204/abstract

The IMA currently recognizes 90 Cr bearing minerals. 16 minerals if you only count those that contain also Si. Feldspar can be either K, Na or Ca-Feldspar. Of those 16 minerals 6 contain Na, 2 K and 5 Ca. Reading those papers might even narrow the choices down to a couple of minerals that can form in standard-toilet-bowl-conditions.

Mineral database that lets you select minerals by their chemistry:
http://rruff.info/ima/

I think that unless you are willing to donate your toilet bowl to science that the answer won't get any more precise than this.

Edit:
Cu would be the favorite choice for a blue color mineral (Azurite, ...). There is also a study about the removal of copper by feldspar:

Experimental studies of the interaction of aqueous metal cations with mineral substrates: Lead, cadmium, and copper with perthitic feldspar, muscovite, and biotite
http://www.sciencedirect.com/science/article/pii/S0016703797001178

Again there are 603 Cu-minerals. Cu+Si=32 minerals. With the common Feldspar cations your left with about 10 each. I don't think the minerals could be recognized visually. The favorite method would be x-ray diffraction of a powder sample of the blue stuff.