Tile over 2x6x1.5 T&G subfloor, spanning 48" beams
Yes add the blocking as you have in your diagram.  

You should also laminate your 2x6 tng flooring with plywood.

Are you doing large format tile?  

The typical requirement for tile is 1 1/4" thick plywood subfloor.  If you have less than this you can have problems with defelection.  A 2x6 is usually 1.5" nominal thickness though older material was actual dimensions so thickness wise you seem ok.  

In your scenario, I'd add the blocking, laminate the floor with 3/8" plywood using construction adhesive and screws, and use a decoupling membrane if you can tolerate the increase in height in the bathroom.

If you can't tolerate that much floor height, add the blocking, see if you have any detectable deflection ( I have 5/8" plywood on 16" centers and bouncing on my floor a friend can see it move @~180 pounds ).  If you still have deflection, I'd go with the 3/8 plywood lamination and a reducer in the door.

Good luck.