Slice bagels in half, remove the guts or bread from the inside and toast.
Put the cream cheese in a medium mixing bowl and using a microplane or box grater, grate radish and carrot into the bowl. Add the red pepper, celery, scallions, bacon and garlic. Season with salt and pepper, and mix until combined.
Spread the cream cheese mixture on the bottom half of the bagel and top with tomato, lettuce and onion, and bagel top.