Piezoelectric materials are utilized for high-power ultrasonic devices such as ultrasonic motors, which are driven under high stress and strain. The nonlinear elastic vibration of piezoelectric materials is a critical problem because it degrades the output performance. (Bi,Na)TiO3-BaTiO3 (BNBT) ceramics are one of the lead-free piezoelectric materials that show outstanding characteristics under high power driving, such as stable mechanical quality factor and resonance frequency. We evaluated the high-power characteristics of BNBT ceramics by measuring complex higher-order elastic constants using a nonlinear piezoelectric vibration model. We found that the absolute value of the higher-order elastic constant of BNBT was less than 4% of Pb(Zr,Ti)O3 (PZT). Additionally, we developed a miniature ultrasonic motor using a BNBT multilayered piezoelectric transducer. This multilayered structure was utilized to enhance the piezoelectric displacement and was equipped with elastic fins, which convert the longitudinal vibration of the multilayered piezoelectric transducer into the rotational moment of the rotor. The rotational speed reached 922 rpm at a preload of 3 N under an input voltage of 58 Vpp and a resonance frequency of 60.0 kHz.