Bevel-tip steerable needles for minimally invasive medical procedures can be used to reach clinical targets that are behind sensitive or impenetrable areas and are inaccessible to straight, rigid needles. We present a fast algorithm that can compute motion plans for steerable needles to reach targets in complex, 3D environments with obstacles at interactive rates. The fast computation makes this method suitable for online control of the steerable needle based on 3D imaging feedback and allows physicians to interactively edit the planning environment in real-time by adding obstacle definitions as they are discovered or become relevant. We achieve this fast performance by using a Rapidly Exploring Random Tree (RRT) combined with a reachability-guided sampling heuristic to alleviate the sensitivity of the RRT planner to the choice of the distance metric. We also relax the constraint of constant-curvature needle trajectories by relying on duty-cycling to realize bounded-curvature needle trajectories. These characteristics enable us to achieve orders of magnitude speed-up compared to previous approaches; we compute steerable needle motion plans in under 1 second for challenging environments containing complex, polyhedral obstacles and narrow passages.