Wide bandwidth for an air-coupled piezoelectric micromachined transducer (PMUT) is important to achieve short pulse transmission and reception in pulse-echo imaging with high axial resolution. Here, we report experimental results on an air-coupled PMUT with high displacement sensitivity up to 5500 nm/V, high 3 dB bandwidth of 20.3 kHz, and correspondingly short transmission time of 0.05 ms, achieved through dc bias tuning. The dc bias controls the polarization and intrinsic stress of the piezoelectric layer, tuning frequencies of two closely spaced resonance modes of the ribbon-shaped PMUT. The modes nearly overlapped when applying small dc bias around ±5 V, enabling wideband and short pulse transmission.