Should I bond neutral to ground in a three-wire service when adding new branch circuits?
When adding a branch circuit, you would never, ever have cause to add any neutral-ground bond anywhere. 

That should only be done as part of a total review and reassessment of your Grounding Electrode System (the network of bare/green wires from your ground bar out to your branches and appliances) and your Equipment Grounding Conductor system (the hefty copper wire heading out of your panel to a water pipe and/or driven-into-earth grounding rod or Ufer). 

That's a pretty important set of systems for life safety, so if it looks like those systems are borked up in any way, seriously consider that review.  

And then when it's done, land your branch circuit neutral wires on the neutral bar, and your ground wires on the ground bar.  If this is definitely the main service panel, they might be the same bar.