Your 3/4″ ply and tile backer will be quite sufficient. As your bar width will be around 2 feet, it will provide a solid base without flex.
When I tiled my kitchen cabinets, I used 3/4″ OSB with 1/4″ backer and the surface is very solid.
If I might recommend using epoxy grout, I think you will be satisfied. It does not get as dirty as regular grout and it creates a great water barrier. My bar back has Italian tiles with white epoxy grout, and I have not had a problem with it yet.
Good Luck,