Many scientific workflow scheduling algorithms need to be informed about task runtimes a-priori to conduct efficient scheduling. In heterogeneous cluster infrastructures, this problem becomes aggravated because these runtimes are required for each task-node pair. Using historical data is often not feasible as logs are typically not retained indefinitely and workloads as well as infrastructure changes. In contrast, online methods, which predict task runtimes on specific nodes while the workflow is running, have to cope with the lack of example runs, especially during the start-up. In this paper, we present Lotaru, a novel online method for locally estimating task runtimes in scientific workflows on heterogeneous clusters. Lotaru first profiles all nodes of a cluster with a set of short-running and uniform microbenchmarks. Next, it runs the workflow to be scheduled on the user's local machine with drastically reduced data to determine important task characteristics. Based on these measurements, Lotaru learns a Bayesian linear regression model to predict a task's runtime given the input size and finally adjusts the predicted runtime specifically for each task-node pair in the cluster based on the micro-benchmark results. Due to its Bayesian approach, Lotaru can also compute robust uncertainty estimates and provides them as an input for advanced scheduling methods. Our evaluation with five real-world scientific workflows and different datasets shows that Lotaru significantly outperforms the baselines in terms of prediction errors for homogeneous and heterogeneous clusters.