The understanding and exploitation of non-linear microbubble signals is an active research area that aims to advance contrast ultrasound into a high sensitivity and specificity diagnostic imaging modality. In order to discriminate the difference between echoes from tissue and contrast microbubbles, it is of particular interest to estimate the reflected signal pulse location in the time domain and its spectral content in the frequency domain. Therefore, a reversible jump Markov chain Monte Carlo (rjMCMC) algorithm, a robust statistical signal processing technique, is introduced in this paper for the analysis of echo signals from Ultrasound Contrast Agents (UCAs). This algorithm provides many advantages over conventional Fourier transform based techniques. Furthermore, our results also show that the frequency components and pulse location can be accurately estimated simultaneously, which assists in characterising the signal content and the design of transmit pulsing regimes in future work.