On Fri, 11 Apr 2014 15:18:05 -0400, BenignBodger
wrote:

Since I'm redoing this bathroom for my
elderly mother any sort of trip hazard is a worry but putting in any of the
threshold pieces I've seen would seem to make it worse by being even
thicker. Any ideas?

I have metal transitions for the doorways to my kitchen, where it goes
form hardwood to thick vinyl sheeting. Kitchen floor is about 1/4
higher. They're 3'' wide and are "stepped" so you couldn't even stub
your toe on the lips.
Got them at a big box, and they were an exact replacement for the old
ones, whose finish was was junked up.
Did it when I sanded the hardwood floors.
They look good and last forever. Cut to size with a hacksaw.