As organizations with existing on-premise infrastructure investments shift to the hybrid cloud computing paradigm, it is imperative to address the various challenges involved. One of the most important issues is the utilization of novel workload scheduling heuristics in order to effectively harness the security provided by the private cloud and the virtually unlimited resources of the public cloud. In this paper, we propose heuristics for the scheduling of real-time bag-of-tasks jobs that arrive dynamically at a hybrid cloud. The proposed scheduling strategies take into account the end-to-end deadlines of the jobs, as well as the monetary cost required for the utilization of the complementary public cloud resources. Furthermore, they take into consideration that some of the component tasks of the jobs may require input data that are sensitive and thus should not be transferred to the public cloud. The performance of the proposed heuristics is evaluated by simulation. For comparison purposes, two widely used baseline scheduling policies are also examined. In the simulation experiments, we consider jobs with either tight or loose deadlines and with different probabilities that the input data of their component tasks are sensitive.