We present a complete and robust framework for non-singular bouncing cosmology in a closed universe (\(k=+1\)). The regularized field space metric \(g^S_{\chi\chi} = (1 + e^{-2\alpha\phi/M_{\rm Pl}})^{-1}\) is derived from fundamental boundary conditions, uniquely emerging as a sigmoid function. This enables a cosmological bounce at finite, sub-Planckian energy density, followed by 60+ e-folds of inflation without violating the Null Energy Condition. Two-field scalar perturbations \((\delta\phi, \delta\chi, \Phi)\) are integrated in the Newtonian gauge directly through \(H=0\), with all sound speeds \(c_\phi^2 = c_\chi^2 = c_T^2 = 1\) verified numerically at the bounce — strict hyperbolicity, no ghost or gradient instability. An independent flat-FRW Mukhanov–Sasaki run reproduces the CMB-scale spectral index \(n_s = 0.9683\) to \(|\Delta n_s| = 5.5\times10^{-4}\) of the exact slow-roll benchmark, and the local non-Gaussianity \(f_{\rm NL} \approx +0.013\) (\(\delta N\) formalism) agrees with Maldacena's single-field consistency relation to \(|\Delta f_{\rm NL}| = 1.5\times10^{-4}\). Predictions are BKL-stable, \(\alpha\)-universal across both baseline and excited-spectator scans, and consistent with Planck (\(n_s \approx 0.967\), \(r \approx 0.003\)).