Bayesian non-negative matrix factorization (BNMF) has been widely used in different applications. In this article, we propose a novel BNMF technique dedicated to semibounded data where each entry of the observed matrix is supposed to follow an Inverted Beta distribution. The model has two parameter matrices with the same size as the observation matrix which we factorize into a product of excitation and basis matrices. Entries of the corresponding basis and excitation matrices follow a Gamma prior. To estimate the parameters of the model, variational Bayesian inference is used. A lower bound approximation for the objective function is used to find an analytically tractable solution for the model. An online extension of the algorithm is also proposed for more scalability and to adapt to streaming data. The model is evaluated on five different applications: part-based decomposition, collaborative filtering, market basket analysis, transactions prediction and items classification, topic mining, and graph embedding on biomedical networks.