This work addresses the problem of creating a Bayesian Network based online semi-supervised handwritten character recognisor, which learns continuously over time to make a adaptable recognisor. The proposed method makes learning possible from a continuous inflow of a potentially unlimited amount of data without the requirement for storage. It highlights the use of unlabelled data for boosting the accuracy, especially when labelled data is scarce and expensive unlike unlabelled data. An algorithm is introduced to perform semi-supervised learning based on the combination of novel online ensemble of the Randomized Bayesian network classifiers and a novel online variant of the Expectation Maximization (EM) algorithm. We make use of a novel varying weighting factor to modulate the contribution of unlabelled data. Proposed method was evaluated using online handwritten Tamil characters from the IWFHR 2006 competition dataset.The accuracy obtained was comparable to the state of the art batch learning methods like HMM and SVMs.