Handwritten character recognition is a crucial task because of its abundant applications. The recognition task of Bangla handwritten characters is especially challenging because of the cursive nature of Bangla characters and the presence of compound characters with more than one way of writing. In this paper, a classification model based on the ensembling of several Convolutional Neural Networks (CNN), namely, BanglaNet is proposed to classify Bangla basic characters, compound characters, numerals, and modifiers. Three different models based on the idea of state-of-the-art CNN models like Inception, ResNet, and DenseNet have been trained with both augmented and non-augmented inputs. Finally, all these models are averaged or ensembled to get the finishing model. Rigorous experimentation on three benchmark Bangla handwritten characters datasets, namely, CMATERdb, BanglaLekha-Isolated, and Ekush has exhibited significant recognition accuracies compared to some recent CNN-based research. The top-1 recognition accuracies obtained are 98.40%, 97.65%, and 97.32%, and the top-3 accuracies are 99.79%, 99.74%, and 99.56% for CMATERdb, BanglaLekha-Isolated, and Ekush datasets respectively.