Since Murray has brought the methods up;
I'd insulate with 3 or 4 layers of masking tape interlaid with paper and with damp rag on top of them, a thin knife for a lever (gently!) and use a (cheap) hot-air gun for heat, or

dig out the screws that those nuts were on, and grind/melt the bridge off with a (cheap) angle-grinder, metal-cutting disc. You'd need a solid piece of steel to keep grinding/cleaning the disc. And safety glasses. And the guitar clamped down. It might generate enough heat to melt the glue anyway. The angle-grinder wouldn't care if you left the screws in, it would just get them red-hot and burn them away.
Routers are far better tools for wood. Far dearer, and far harder to control in this situation. And you definitely have to get rid of any metal before you use them.
I still say you need another bridge before you start.