Bangla language consists of fifty distinct characters and many compound characters. Several notable studies have been performed to recognize Bangla characters, both handwritten and optical. Our approach uses transfer learning to classify the basic, distinct, as well as compound Bangla handwritten characters while avoiding the vanishing gradient problem. Deep Neural Network techniques such as 3D Convolutional Neural Network (3DCNN), Residual Neural Network (ResNet), and MobileNet are applied to generate an end-to-end classification of all possible standard formations of handwritten characters in the Bangla language. The Bangla Lekha Isolated dataset, which contains 166,105 Bangla character image samples categorized into 84 distinct classes, is used for this classification model. The model achieved 99.82% accuracy on training data and 99.46% accuracy on test data. Comparisons with various state-of-the-art benchmarks of Bangla handwritten character classification show that the proposed model achieves better accuracy in classifying the data.