According to CJ :
The power is shut off in the house... It is being remodeled. And, I
misspoke about grounding the breaker in the panel, otherwise I was
looking for alternate ways of wiring up the bath and updating the wires
to the bath.

With 60 AMPS coming in and currently 15 + 15 Amps in the three rooms,
adding a 15 or 20 Amp breaker to the box won't affect the main breaker
in terms of tripping. The most going thru the three rooms would be 50
AMPs if a 20 AMP breaker and 12/2 was added to the bathroom.

You seem to be under the impression that the sum of breaker ratings on
each leg of the main needs to be less than the main breaker. It doesn't.
The breaker ratings are maximums, and circuits seldom draw that much.
Try to balance things in terms of expected/routine large loads, and
don't worry about sum-of-breakers. Mind you, 60A is mighty small these days.

The level of questions you're asking suggests to me that you need
to read a good book on electrical wiring, or, hire someone to do
the work. If you're asking about color codes, and not familiar with
what "14/3" actually means, I _really_ worry about what you're NOT
asking about and should be.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.