How to handle a 2" step into bathroom?
Given the nearby stairs and doorways, raising the floor outside the bathroom obviously isn't a good option. The only thing to do now is fashion a transition strip. 

Given the already extreme height of the transition, a typical L-molding (that would lap onto the tile) is inadvisable. I'd use a heavy piece of finished hardwood that coordinates with your home's trim and simply stand it along the face of the step. It could be 3/4" stock, but 5/4 or two-by would probably look better at that height.

____________________
           |         \
           |          \
  bathroom |  trans.   |
  floor    |  strip    |
           |           |
           |           |
           |           |
           |           | 


How much bevel you use depends on the orientation of the transition with respect to the door opening. I'd consider tapering it down up to an inch if you have room inside the door jamb. I'd seek to avoid having the transition strip protrude into the hallway past the jamb edges.

Use construction adhesive to fasten it in place, then use a color-matched caulk to act as grout between the tile and the wood. A smaller gap is better here, regardless of the grout line width.