How should I handle reflooring the bathroom of an old house?
Two things here.

If you don't want squeaks...   First you should remove plywood and add blocking to the joists.   The swaying of the joists, even slight allows the screws to move and eventually squeaks.   Second you need to glue the first layer of plywood down.

Your calculations are off - kind of by a lot - AND you are committing poor design thoughts at the beginning.

you should have a threshold in the bathroom between the hardwood and the tile
this threshold should sit higher than both - 1/4&quot;
the reasoning is a flood should stay in the bathroom
yes you are building a mini pool!
based on your joists I would start with 3/4&quot; plywood
Big Issue - no calculation for the thinset.   With bigger tiles this can get to be over 1/4&quot;.   Rather significant.   You will be troweling and back buttering.
Another Big Issue - no calculation for the thinset for the Ditra install!!!  This will be at least 1/8&quot;
So with 3/4&quot; plywood, ditra, and tile you are at 1.5&quot; conservatively... possibly over.
so this threshold needs to be at least 1&quot; so that it may hide the fact that your tile might be slightly higher than the wood.
if back buttering the tile, you are probably going to need to put down less thinset with your trowel (under spec).