The understanding and exploitation of acoustic echo signals from nonlinear ultrasound scatterers is an active research area that aims to improve the sensitivity and specificity of diagnostic imaging. Discriminating between acoustic echoes from linear scatterers, such as tissue, and nonlinear scatterers, such as contrastmicrobubbles, based on their frequency content is also an important topic in ultrasound contrast imaging. In order to achieve these objectives, a fundamental preliminary stage is to extract information about the reflected signals in the frequency domain with high accuracy: this is essentially a feature extraction and estimation problem. In this paper, a parametric Bayesian spectral estimation method is utilised for the analysis of the backscattered echo signals from microbubbles. In contrast to existing nonparametric discrete-Fourier-transform- (DFT-) based spectral estimation techniques used in the ultrasonic literature, this method is able to estimate the number of spectral components as well as their amplitudes and frequencies. The Bayesian spectral analysis technique has improved frequency resolution compared with the DFT for short multiple-component signals at low signal-to-noise ratios. The performance of the method is demonstrated with simulated signals, as well as analysing experimentally measured echo signals from nonlinear microbubble scatterers.