Recognition of Bangla handwritten characters is a difficult but important task for various emerging applications. For better recognition performance, good feature representation of the character images is a primary requirement. In this study, we investigate a recently proposed machine learning approach called deep learning [1] for Bangla hand written character recognition, with a focus on automatic learning of good representations. This approach differs from the traditional methods of preprocessing the characters for constructing the handcrafted features such as loops and strokes. Among different deep learning structures, we employ the deep belief network (DBN) that takes the raw character images as input and learning proceeds in two steps — an unsupervised feature learning followed by a supervised fine tuning of the network parameters. Unlike traditional neural networks, the DBN is a probabilistic generative model, i.e., we can generate samples from the model and it can fit both the semi-supervised and supervised learning settings. We demonstrate the advantages of unsupervised feature learning through the experimental studies carried on the Bangla basic characters and numerals dataset collected from the Indian Statistical Institute.