Place bacon pieces in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon on paper towels. Crumble once cool enough to handle.
Season chicken pieces lightly with salt and pepper.
Grease the bottom of a slow cooker with bacon grease and layer 1/2 of the potato nuggets on the bottom. Sprinkle with 1/2 of the bacon bits. Mix Colby cheese and Monterey Jack cheese together in a bowl and sprinkle 1/3 of the cheese mixture on top. Add chicken in 1 layer and top with 1/2 of the remaining cheese mixture. Sprinkle with remaining bacon bits and top with remaining potato nuggets. Sprinkle rest of the cheese mixture on top and pour milk over everything.
Cover the slow cooker and cook on High until chicken is cooked though and cheese has melted, 3 to 5 hours.