Will the assault ratings stack? I know way states gains assault two, not +2 assault, but I’m curious.

Way of the Bear: This creature gains assault 2. (Before this creature attacks, deal 2[D] to the attacked enemy.)
Ancient Bear: Assault 2. (Before this creature attacks, deal 2[D] to the attacked enemy.)

In the rulebook under Assault:
"If a creature with the assault (X) keyword gains another instance of the assault (X) keyword, the two X values are added together."

So yes, the Ancient Bear would have an assault of 4.

10 second look in the rules book under assault "If a creature with the assault (X) keyword gains another instance of the assault (X) keyword, the two X values are added together". So yes they add up.