We present a bus arbitration scheme for soft real-time constrained embedded systems. Some masters in such systems are required to complete their work for given timing constraints, resulting in the satisfaction of system-level timing constraints. The computation time of each master is predictable, but it is not easy to predict its data transfer time since the communication architecture is mostly shared by several masters. Previous works solved this issue by minimizing the latencies of several latency-critical masters, but the side effect of these methods is that it can increase the latencies of other masters, hence they may violate the given timing constraints. Unlike previous works, our method uses the concept of "slack" in order to make the latency as close as its given constraint, resulting in the reduction of the side effect. The proposed arbitration scheme consists of bandwidth-conscious arbiter and scheduler. The arbiter can be any existing bandwidth-conscious arbiter and the scheduler implements the latency-awareness proposed in this paper. The scheduler is involved in the arbitration only when it observes a request whose slack is not sufficient for the given timing constraint. The experimental results show that our method outperforms the conventional round-robin arbiter by more than 100% in the best case in terms of the longest violated cycles.