Tile – Want to retile the bathroom, but found masonry filling under old tile

You got the right idea, but I'd opt for adding a double 2X? between the existing joists at either end of the bathroom span and fill in with an extra joist making your spacing 12 inches on center instead of 24. Add a couple of perpendicular stiffeners, and you will have a good stable base for your new 3/4" sub-flooring. Tile needs a good solid base or your grout will crack every time.

The vapor barrier is not so important on the floor, however, if you are doing new walls, a properly installed vapor barrier is very important. There are several methods of adding a vapor barrier, depending on what types of tile backer you plan to use. Think of it as a system and get all the right layers on in the right order.

One comment on the advice you read is that I don't see a thing in there about deflection - evidently Mike Holmes is sure that if he merely has 1-1/4" of subfloor, all is good. Real tile specs tend to involve a concept called deflection, and that's the distance part of the floor system moves when loaded, relative to the span you measure over. L/360 is a typical spec - L/180 is twice as bad. (It's usually a lowercase L, but on the computer I'm using a capital to be clear that it's an L.) I happen to have a 3/4" subfloor that's L/587, so it really doesn't need another half-inch on that basis.

Consider what a tile manufacturer has to say... (I'm not going to cut and paste their extensive text here, or rewrite it all) but for one thing they specifically mention setting the backer board in a mortar bed, not "gluing" it down. I'd also venture to sneak in that if you really want "the best" (and will you pay for it these days) look at the "old fashoned mortar bed" (TCNA (Method F145-02)) mentioned at the end of their article. That, of course, means you need to establish an adequately rigid base 3/4" or 1-1/4" + tile thickness below the surrounding floor level, which is why it's not popular these days. But it was a VERY good method, as a lot of old houses demonstrate.

Kinsman Tile