Tile to Tile transition

I am considering retileing over existing tile on a bathroom floor. The problem is it will create a 3/8th inch difference between the bathroom tile and the adjoining hall tile. Any ideas on how to handle this transition without removing the existing floor tile in the bathroom? Have thought about bullnose tile or a wood transition strip to match the door, casing and baseboard?

Have thought about bullnose tile or a wood transition strip to match the door, casing and baseboard?

There ya go. Options are limited in this case.

You could remove a small portion of the bathroom tile and slope to the hallway.

Hollywood saddle.

Schluter reducer edging.