Is bounded waiting satisfied in this 2 process solution?
Bounded waiting is satisfied, the process $p_i$ will never be bypassed by $p_{1-i}$ after changing the value of $w_i$ (wants $i$) to $1$.

If $p_i$ set the value of $w_i$ to $1$, then in order to enter the critical section, $p_{1-i}$ must pass the while loop. This cannot happen until the value of $w_i$ is set to 0. The only place where $w_i$ is set to $0$, is after $p_i$ has finished, which means he will never be bypassed by $p_{1-i}$.

When in doubt, try to prove it yourself. If you agree that the number of times a process may be bypassed is at most $0$, then yes, bounded waiting holds.