In this paper we present a new memetic algorithm, which is called Discrete Bacterial Memetic Evolutionary Algorithm for solving the Traveling Salesman Problem with time windows (TSPTW). This method is the combination of bacterial evolutionary algorithm with 2-opt and 3-opt local searches. The algorithm was already tested on symmetric Traveling Salesman Problem (TSP) benchmark instances up to 5000 cities. It showed good properties in terms of tour lengths, runtimes and predictability of runtimes, so we decide to examine other variants of TSP with our algorithm. With some slight modifications our method was tested on TSP with time windows benchmark instances. Our test results were compared with the state-of-the art methods. In most cases our algorithm found the best-known solutions, and in terms of solution quality and runtime it is the second best method.