Add a 1/2" BC sanded or plugged ply or 3/8" for that matter. Get the heat mat that's a waterproof membrane as well set in thinset bed and tile over the mat.. Make shore your 2nd ply layer is staggered correctly on joists.

Joist span?

Tile and stone floors do not tolerate the normal movement allowed in a wood floor.

Look around the John Bridge forum for guidance on floor substrate thickness.

Cement board does NOT increase floor stiffness.

It's a bathroom so most likly is 16oc the question is are the joists 2x8, 2x12? Ect... Need at least 1" of wood for any tile install. 1/2" & 3/4" of ply is plenty. Can actually install heat lines over the backer board here is how.

http://floorelf.com/how-to-install-suntouch-warmwire-in-floor-heating-part-1

The actual joist span and height are more important than the joist spacing.

the joist spacing does drive the required subfloor stiffness, with 24 inch spacing needing even more thickness than 16 inch spacing.

If the joists are at the limit of span, no amount of thickness from the subfloor is likely to eliminate joist flex adequately for tile.