Bicycle route planning is a challenging problem because of the diverse set of factors considered by cyclists in choosing their cycling routes. We provide a solution to this problem based on a formal model expressive enough to represent transport network features and cyclists' preferences grounded in the studies of real-world bicycle route choice behaviour. Our solution employs the A* algorithm together with vectors of cost and heuristic functions – able to optimise routes for travel time, comfort, quietness, and flatness. We have implemented, practically deployed and experimentally evaluated our solution in the challenging setting of the city of Prague. The experiments confirmed that the planner is able to return high-quality plans in less than 250 milliseconds per query.