Interesting...usually when you choose to remove an icon from the dock, for an application that is running, it will not actually remove unless the app quits. Did you actually go to the work of killing DB and then remove it? 😱
But yeah, anyway, you can drag anything in the apps folder to the dock, as well as documents, and you can drag folders themselves to the dock, but only on the extreme right, just left of the trash. If a program is running, and its icon is not normally in the dock, you can get it to stay there by either holding the mouse button over it and selecting Keep in Dock from the menu, or by dragging it to a position other than the one its currently in, in the dock (apps that are not "kept" in the dock will be on the extreme right, so if you drag them to a spot on the left, they will stay on the dock in that position).