Simmer 1 cup Bloody Mary Mix over medium heat until reduced and slightly thickened (will be about 2/3 cup). Keep warm on stovetop.
Meanwhile, toss together cheeses, celery, and green onion in small bowl. Set aside.
Blend beer batter ingredients together in a shallow pan. Set aside.
Lay out 4 pieces of bread. Cover each piece with some of the cheese blend. On two of the slices, place bacon and top with more cheese blend. On the other two slices layer banana peppers and pickles, top with more cheese blend. TIP: At this point, microwave or broil open-face just until cheese begins to melt. This will help hold sandwich together through next steps.
Put each of the two sandwich sides together, cheeses and fixings to the middle. Preheat griddle to medium-low heat. Melt butter on griddle. Dip each sandwich into beer batter, then flip to dip opposite side. Place on griddle and cook slowly 3-4 minutes on each side, until golden brown. Serve with Bloody Mary Dipping Sauce.