I do not take Pistols to Gunsmiths. I would take it to a Pistolsmith. However, any smith can cut that bushing out with an end mill. If it was made back in 1882, and it hasn't been messed with by some Klutz, it is a very valuble gun and if you start messing with it, it will lose most of it's collector value.
Having said that, you have a couple of options. You can haver a smith replace that bushing with a Uberti part which will be inexpensive, or maybe a Uberti Part from Colt that will buckle your knees. The Uberti parts are available from Cimarron Arms.
If you can get it out of there, Ron Powers makes some shims that will take the endshake out of it and they are really easy to install.
I recently restored a 1910 Colt SA by installing all new Uberti Parts. The gun belonged to the man's grandfather who bought it new and a brother in law had destroyed it. Every smith in Arizona said it could not be fixed, so I did it, of course. The parts ran about $160.00 and it took a lot of time to get it right, but now it runs like new. I told him since it had been reblued, rebarreled, and ruined that it had no collector value and it was a $500.00 gun when I finished it. It was a loser for me , but that man was a happy camper when he picked it up. The job was $285.00 and took about 10 hours. I am not known to be a good business man. I just love it when it can't be done! The cylinder bushing was ruined in this one, too. I did get it out, however.