This paper presents an any-time scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power is in that it can use any available scheme that bounds the probability of evidence, enhance its performance in an anytime manner, and transform it effectively into bounds for posterior marginals. The scheme is novel in that using the cutset condition principle (Pearl, 1988), it converts a bound on joint probabilities into a bound on the posterior marginals that is tighter than earlier schemes, while at the same time facilitates anytime improved performance. At the heart of the scheme is a new data structure which facilitate the efficient computation of such a bound without enumerating all the cutset tuples. Using a variant of bound propagation algorithm (Leisink and Kappen, 2003) as the plugged-in scheme, we demonstrate empirically the value of our scheme, for bounding posterior marginals and probability of evidence.