Preheat the oven broiler.
Prep the ingredients per instructions above.
For the cucumber water, place the cucumber slices in a pitcher with water. Let infuse in the refrigerator. Serve over ice if desired.
Combine the sauerkraut and dressing in a bowl.
Warm the corned beef in a nonstick pan over medium heat.
Place bagels, cut side up, on a baking tray. Divide cheese among bases of the bagels. Broil for 3 - 4 minutes until the bagels are golden and the cheese is melted and bubbling.
To assemble, place corned beef and sauerkraut mixture on the bagel, and top with another bagel half. Cut in half.
Serve reuben bagels with barbecue chips, pickle. and cucumber water.