During recent years, the concept of attention in deep learning has been increasingly used to boost the performance of Speech Emotion Recognition (SER) models. However, these models for SER exhibit shortcomings in jointly emphasizing the time-frequency and dynamic sequential variations, often under-utilizing the rich contextual emotion-related information. We propose a hybrid deep learning model for SER using Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory Networks (BiLSTM) with multiple attention mechanisms. Our model utilizes features from the speech waveform viz. Mel spectrograms and Mel Frequency Cepstral Coefficients (MFCC), along with their time derivatives as input to the CNN and BiLSTM modules, respectively. A Time–Frequency Attention (TFA) mechanism, optimally incorporated into CNN, helps to selectively focus on emotion-related energy–time–frequency variations in Mel spectrograms. Attention-based BiLSTM uses MFCC and its time derivatives to identify the positional information of emotion for addressing the dynamic sequential variations. Finally, we fuse the attention-learned features from the CNN and BiLSTM modules and feed them to a Deep Neural Network (DNN) for SER. The experiments were carried out using three different datasets: Emo-DB and IEMOCAP, which are public datasets, and Amritaemo_Arabic; a private dataset. The hybrid model exhibited superior performance on both the public and private datasets, generating an average SER accuracy of 94.62%, 67.85%, and 95.80% with Emo-DB, IEMOCAP, and Amritaemo_Arabic datasets, respectively, effectively outperforming several state-of-the-art models.