Quantitative ultrasound is a modality that is used to evaluate bone quality. It is considered that the analysis of ultrasound guided wave propagating along cortical bone may be useful for the assessment of cortical bone quality. Because the frequency-dependent wavenumbers reflect the elastic parameters of the medium, high-resolution estimation of the wavenumbers at each frequency is important. We report an adaptive array signal processing method with a technique to estimate the numbers of propagation modes at each frequency using information theoretic criteria and the diagonal loading technique. The proposed method estimates the optimal diagonal loading value required for guided wave estimation. We investigate the effectiveness of the proposed method via simple numerical simulations and experiments using a copper plate and a bone-mimicking plate, where the center frequency of the transmit wave was 1.0 MHz. An experimental study of 4 mm thick copper and bone-mimicking plates showed that the proposed method estimated the wavenumbers accurately with estimation errors of less than 4% and a calculation time of less than 0.5 s when using a laptop computer.