Place tenderloin in a non-reactive container. Whisk together olive oil, garlic, shallots, rosemary and vinegar. Pour marinade over tenderloin and place in refrigerator for 8 hours.
Peel and roughly chop the beets. Place in sauce pot with bay leaf, chicken stock, and salt. Simmer until beets are tender. Place mixture in blender and puree until smooth. With machine running, crumble in the blue cheese. Remove beet sauce from blender and adjust seasoning with salt and pepper. Cover and refrigerate until needed.
Heat grill. Grill tenderloin until medium rare, about 20 minutes total, turning the tenderloin to cook evenly. Let tenderloin rest for 10 minutes before slicing into 12 (4-ounce) pieces. Drizzle beef with beet sauce and garnish with arugula and serve.