Set a skillet over medium heat and cook the bacon until crisp. Transfer to a paper towel-lined plate and allow to cool.
Drain all but 1 teaspoon of the bacon fat from the pan. Add the jalapeno and cook until softened, about 1 minute. Transfer to a small bowl to cool.
Preheat the oven to 450°F.
In a large bowl combine the flour, baking powder, baking soda and salt. Scatter the butter over the top, and using your fingertips, rub it into the flour until the mixture is mealy, and pea-sized pieces of butter remain.
Add the bacon, jalapeno and cheese to bowl. Pour in the chilled buttermilk and stir just until the dough comes together. It will still be sticky and wet, which is okay.
Liberally dust a work surface and turn the dough out. Dust it with flour and shape into a circle, 8”–10” in diameter and 1” thick. Using a 2” floured cookie cutter or glass, cut out biscuits. Place them on a baking sheet and bake for 15–20 minutes, or until puffy and golden brown.