If it were my bell, I’d give it a good washing with soap and water to clean the dirt off of it. You might want to try using a wooden toothpick to scrape off the dirt around the ridges before you dry the bell. That’s not to say that I would polish it with brass polish, however. Some collectors like their bells to be shiny. Others value the natural patina that develops over the years.
Next I would write down the significance of the bell so future generations will know the bell’s history of being passed down through the generations from family who immigrated from Sweden. Keep that information either with the bell or in a place where your descendants can find it.
Lastly, I would place the bell in a place where it’s visible to others. The bell and its story will make a great conversation piece to your guests, especially when you tell them it’s a family heirloom!