We derive theoretical bounds on expected hitting times in densely covered delay-tolerant networks (DTNs). We consider a number of fixed (data collector) nodes deployed in the DTN region, and a number of mobile (data generator) nodes that move freely in the region according to Brownian motion. As it moves, each mobile node is assumed to continuously generate and buffer data. When a mobile node comes within the communication coverage range of a data collector node, it downloads its buffered data to it. Otherwise, it keeps generating and buffering its data. In this paper, we derive analytic bounds on the amount of time a mobile node spends without communication coverage. Then, using these derived bounds, we derive sufficient conditions on node density that statistically guarantee that the expected hitting times remain below a given threshold.