davismanLV said:
...what is the normal procedure? Finish the top and then glue on the bridge? And what kind of glue do you use in that case?...
What George said.
In addition to hot hide glue, bridges are also glued on with aliphatic resin (yellow) glue. Typically, the raw wood is masked off with removable tape in the exact area in which the bridge is to be applied, although some luthiers finish the top first and then strip, scrape, sand, or rout off the finish. The bridge is then glued and clamped in place, either through the sound hole or with a vacuum clamp.
The objective is to have the bridge adhere to raw wood, as you pointed out, but you want it to appear as though it is setting on top of the finish, with a perfectly clean line where the bridge meets the top. You can image what it might look like off the bridge was glued on first and the finish was applied over the top and the bridge. The finish would glop where the bridge meets the top like cove moulding, and subsequent movement between the two distinct surfaces would eventually crack the finish.
Note: The secret to a perfect appearance is to have the finish creep under the bridge just the tiniest amount, versus ending precisely where the bridge begins.
Christopher