It is more work than you previously asked them to do, thats why they want even more money now.. Because they have to strip and remove the diff again, now replace the bushings and then refit everything = Much more work than before.
The old bush's could give issues when removing it and refitting the new ones, this alone can/may take hours so no one can really say to you: "Yes sir, i can do everything and have your car back 100% in X hours" because, there are other gremlins that can surface when you start working on an old car and since all mechanics/workshops charge by the hour, they cannot give you a straight up price without even checking your car. stripped bolts, worn parts, ect can also delay the job or add additional costs..
Any honest mechanic will tell you all this upfront. I always make it known to customers from the onset and if they dont like it or are looking for cheap and quick labor, they must take their car to whoever fits their situation.