Place the softened cream cheese in a mixing bowl and mash it until smooth.
Add the shredded cheddar cheese, bacon bits, chopped chives, and garlic powder. Stir until everything is evenly combined.
Sprinkle in the paprika and mix again to distribute the color and flavor.
Turn the mixture out onto a sheet of plastic wrap. Shape it into a round ball, then use your fingers or the edge of a spatula to press light vertical ridges around the sides so it resembles a pumpkin.
Cut a small stem from the green bell pepper and press it gently into the top center of the cheese ball.
Wrap the cheese ball in plastic wrap and chill for at least one hour to firm up.
Unwrap and place on a serving plate with the crackers arranged around it.