Bionic wavelet transform is a continuous wavelet, based on adaptive time frequency technique. This paper presents a speech recognition system for recognizing isolated words by discretizing the continuous Bionic Wavelet (BW). Conversion from continuous to discrete is achieved by adopting central frequency and thresholding techniques. The BW features of noisy signal are processed through MFCC to obtain the optimal features of the speech signal. SVM, Artificial Neural Network (ANN) and LSTM techniques are used to improve the recognition rate by enhancing the speech signals. The experiments are conducted on FSDD and Kannada data set. The speech feature vector is calculated using the parameters extracted by Bionic wavelet with different central frequencies of Morlet, Daubechies and Bior3.5, coiflet5 mother wavelets. The obtained Bionic-MFCC optimal features are fed to SVM, ANN and LSTM models for the classification and recognition process. The performance of the models is tabulated for correct recognition that varies from 95% to 96% among these models. The models are tested for various SNRs noise levels like 5 dB, 10 dB, 15 dB and the recognition accuracies of these models are presented for convoluted noisy speech data.