This paper addresses the problem of estimating the instantaneous frequency (IF) and amplitude of the modes composing a non-stationary multi-component signal in the presence of noise. A novel observation model for the signal spectrogram is developed within a Bayesian framework to handle intricate configurations involving noise or overlapping components. The model parameters are estimated using a stochastic variant of the Expectation-Maximization algorithm, bypassing the computationally expensive joint parameter estimation from the posterior distribution. We then design an algorithm for instantaneous amplitude and frequency estimation that accounts for overlap and amplitude variations of the components. To assess the performance of the proposed method, we conduct experiments on both real-world and simulated signals, involving separated or crossing modes. The benefits of our method in terms of efficiency compared with several state-of-the art techniques appear to be significant in that latter case, but also when the amplitude of the components are varying across time.