Generally I've only ever seen a combination of DR + bearings done when there's literally nothing available to observe, but the skipper (even when it's the same person navigating, which is pretty common in modern civilian shipping) demands that an observation be made (e.g. post sunset, in a storm, during a new moon in the open ocean).
It's similar to Sumner Line observations, but isn't as reliable. In theory it can be more accurate than the Sumner Line, but relies entirely on instrumentation being precise (fun fact, it usually is anything but). It's possible, given the way that latitude and longitude are calculated, to use nothing more than the ship's compass and knowledge of how fast you're moving, and in which direction, to get a reasonable approximation for where you're at in the world, provided you have a DR or direct observation as a reference point. The *big* problem with this is that if you're not moving at the speed you think you are, or if your compass isn't corrected (or at least the calculations for your compass bearing isn't corrected for any deviations) you can be off by hundreds, if not thousands of miles (depending on how fast your ship can travel, and how long you've gone between observations.
Still, even with the inherent potential for winding up *way* off course, a good navigator working with reliably accurate instrumentation, can calculate out a reasonably accurate position, generally within a few miles or so of the actual location. This sounds pretty bad, when you look at something like a sat-nav being accurate within 30-40 meters (or better), but when you're talking about human beings, calculating all of this out by hand (since calculators didn't exist yet), being within a dozen or so miles of the actual position, in a target area of thousands of square miles, that's pretty good. At the very least, the position they calculate for would be visible from the deck.