Can I have the bridge removed and the decay fixed and then re-cemented or will I need a new permanent bridge?

Hi:Normally in order to remove the bridge it has to be cut and can not be reused.  Also if the decay is around the margin of the tooth the existing bridge would not protect the tooth appropriately.  A new bridge is necessary to have a good seal.Best,Dr. Maddahi

Assuming that there is decay... it is almost always at or extending beyond the margin of the crown/bridge margin. This is the critical area that needs to be sealed for long term stability of the bridge (new or existing). Sometimes small cavities can be filled at the margin of a bridge if it can be accessed easily, however one never knows if ALL the decay was removed when this is done because you can’t see underneath the bridge. 
In heroic situations I’ve replaced bridge over a repaired abutment and it has worked... usually get burned long term trying to do that.
Consider implant and avoid the long term issues with a bridge? May be your best long term option!

Hello,
Nice too meet you.
If you have cavities in long term although it looks perfect, you going to receive problems with your root canal, gum, and inclusive with your bone. So I recommend you to change it as posible yo can.
Best Regard and good luck,
Alfonsina Hernandez R. MD

Hello,
You Need to replace the bridge. It doesn’t matter the bridge looks in good condition, you Will Need a New one as your doctor said. 
Dr. Franco
DentArtist Clinic