Right now bathroom light switch is inside in the corner, I'd like to move it outside so a corner shelf can go where it is now.

It's going just on the other side of the wall, anything I should pay attention to here..

Also, I need to install a light close to the bath tub but closest power box is on the other side of the bathroom, what's easiest way to do this? My plan is to simply "dig in" cable into the wall, drywall it, paint it (since I'll be painting whole bathroom anyway).

Switch
Remove switch, cut nails of existing box. Remove box.
Cut opening on other side of wall and install old work box. Reinstall switch.


Don't know what you mean by "dig in" cable to wall. More information please. Like drywall or plaster, access to ceiling above or underneath floor?

You will need to pull the wire out from the existing location and relocate it either from the attic or from below. You cannot just bury it in the wall and cover it up.

Some building codes are touchy about light switch locations. Before you do anything check with your local building inspector about where a bathroom switch can be located. That light close to a bath tub is a bit vague, how close because this can also be governed by code. I also agree, don't do any digging and burying.