Unlike Gibson's ES-335, which had a solid block of maple running down the middle of the semi-hollow body, which made mounting the pickups and installing a stop tailpiece and tune-o-matic bridge a breeze, Gretsch's hollowbodies were just that, hollow. Almost all of these had Bigsby tailpieces, which were screwed into the wood along the back edge, right where you'd have the rear strap button. This allowed the tailpiece to swing loose away from the top if there were no strings to hold it tight (other Bigsby models had screw mounts that held the unit in place). Somewhere early in the development of these instruments, the decision was made to not mount the bridges to the tops of the guitars. Someone probably knows why that decision was made, but for most of us, it's somewhat of a mystery. Like the Bigsby, string pressure held the bar bridge, which sat on an ebony base, firmly in place (and keep in mind that back in the 1950s and '60s strings were heavy gauge - the light gauge or "slinky" sets didn't appear until the late 1960s and into the 1970s). As long as you changed your strings one at a time, there was never an issue. But many of us simply removed all the old strings in preparation for installing a new set. When we did that, invariably the bridge would slide off and fall to the floor. It was easy enough to slide it back once you had most of the strings on, but unless there was some sort of light mark to indicate where the bridge was set, we simply had to slide it around until the intonation seemed right - a task much harder than you might think.
After enduring this for a dozen times, most of us did the simplest thing and made a very light mark on the guitar's top that indicated the correct position of the bridge. We're more respectful of our instruments today, so the best way to ensure your bridge will stay in place when the strings are off is to put double-sided tape on the bottom of the wooden base. It can't be too sticky, or you run the risk of pulling off a chunk of the guitar's finish if you're in a hurry. Double-sided painter's tape works well. You just want it to not shift around rather than be stuck to the top forever. It's a simple solution for a rather simple problem that's been vexing guitarists for half a century or more!