Fill a large pot with water and bring it to a boil. Add the small red potatoes and boil until they are fork-tender, about 10 minutes.
While the potatoes are boiling, preheat your oven to 400°F (200°C).
Once the potatoes are cooked, drain and let them cool slightly. Cut each potato in half and slice a small portion off the rounded end so that they can sit upright on a flat surface.
Carefully scoop out the insides of each potato half and place the potato flesh in a bowl. Add the bacon, shredded cheese, and melted butter to the bowl. Mix until well combined and season with salt to taste. Sprinkle a little salt over the potato halves as well.
Spoon the potato mixture back into the hollowed-out potato halves and arrange them on a baking sheet lined with a silicone mat or parchment paper. Place the baking sheet in the preheated oven and bake for about 10 minutes, or until the tops are golden and bubbly.
Remove the Irish Potato Bites from the oven and serve warm, topped with a dollop of sour cream if desired.