Yes, by all means POLISH IT!
Specifically, get a bottle of 3M's "Tarnishield" silver polish to do the job. Tarnishield has a tarnish inhibitor that really slows down future build ups and most folks use it.
BTW, I suspect the INSIDE of the bell is not silver . . . but is actually a "gold wash." Many of the Conns did this and the look is gorgeous.
Because the gold wash is a very light plating of gold over the silverplate, silver polish will buff it off in fairly short order . . . leaving the inner bell increasingly lighter in yellow.
So, if it IS gold wash, try two things to bring out this desirable luster.
1. First, if the horn is tarnished and dirty, polish the silver parts only.
2. Then, after the silver looks great, CLEAN the inner bell part (that's visible in gold wash) with a light coating of WD-40. Just rub it on with your finger tips, gently working it into the surface. After a couple of minutes, GENTLY wipe it off with a soft cotton cloth. This will make it look GORGEOUS and it will look really nice.
3. Finally, if you wish, lightly wipe some "Tarnishield" silver polish onto the inner bell. DO NOT BUFF, but allow it to totally dry.
Let is sit on the gold wash part for a few hours . . . for the Tarnishield's ingredients will actually brighten the silver underparts but not take off the gold this way.
Then, gently rise all the residue off with water . . . gently wiping it off under running water with your fingertips only.
Once the residue is off, PAT DRY ONLY with a soft cotton cloth.
Hope this helps,
Tom