The bridge on my acoustic 12 string was held on by both glue and screws. The screws were under 'pearl' dot inlays, and there were little nuts on the inside which I could easily reach once I'd taken all the strings off. I was instructed to make a cardboard shield to cover the face of the guitar around the bridge, then gently heat the bridge with an incandescent bulb. A little bit of pressure then popped the bridge right off. Use regular white wood glue to attach a new bridge. If you are trying to reattach the old bridge, you'll have to use super glue or crazy glue.
Middle aged carpenter, October 2014