Wrap the sweet potato with a damp paper towel and microwave on high until very soft, 3 to 4 minutes. Transfer to a bowl, mash with a potato masher and set aside to cool.
Meanwhile, in a medium skillet over medium heat, cook the bacon until golden and crisp, about 8 minutes. Use a slotted spoon to transfer bacon to a paper towel-lined plate, then set aside to cool.
Carefully set aside 2 tablespoons of bacon drippings from the skillet.
Preheat oven to 375 degrees F. Line a large baking sheet with parchment paper.
In a food processor, combine the flour, baking powder, sugar, baking soda, salt, and allspice and pulse a few times. Add the cubed butter and pulse to make a coarse meal with a few pea-sized pieces.
Transfer mixture to a large bowl and gently mix in the bacon, buttermilk, and 1 cup of the mashed sweet potato (save any remaining potato for another use).
Transfer mixture to a floured work surface and knead a few times to form a dough. Pat the dough to about 1-inch thick, then gently fold in half. Gently repeat 4 more times.
Roll the dough out to 3/4-inch thick, then use a floured 2 1/2-inch biscuit cutter to cut dough into biscuits, arranging them on the prepared baking sheet.
Gather the scraps and repeat to make a total of 12 biscuits.
Bake until the biscuits are browned and a tester comes out clean, 15 to 18 minutes.
Meanwhile, combine the softened butter, honey, and reserved bacon drippings, mixing until smooth. Add salt to taste.
Serve the biscuits with the honey butter on the side.