The fit between the bridge and the soundboard on a bowed psaltery is important, and should be as snug as possible. Even though all the strings are pressing down on the bridge, if the bridge is in any way uneven, firm contact will not be made.
One technique that is commonly used on stringed instruments is shown below – and adapted to the bowed psaltery:
Basically, a sheet of sandpaper is clamped to the top of the psaltery, and the bridge is carefully stroked in one direction away from the clamps. You can flip the bridge over and see how much of it is being sanded. If the sandpaper is only making contact with the bridge in a few places, this means that things are still uneven. Once the sandpaper is sanding away material along the entire length of the bridge it is ready to be fitted to the psaltery.