If necessary, cut bison brisket to fit into a 6-quart slow cooker.
Sprinkle bison brisket with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper.
Place carrots, parsnips, turnips, and onion in the cooker. Top with bison brisket.
Combine beer, horseradish, garlic, thyme, the remaining 1 teaspoon salt and the remaining 1/4 teaspoon pepper in a medium bowl; pour over bison brisket.
Cover and cook on low for 10 hours. Stir in apricot halves. Cover and cook for 2 more hours.
Transfer bison brisket to a cutting board. Slice bison brisket across the grain; arrange on a serving platter. Using a slotted spoon, transfer vegetables to the platter, reserving cooking liquid. Strain cooking liquid and pass with bison brisket and vegetables.