In a medium saucepan, cook apple, celery and onion in hot oil over medium heat for 6 to 8 minutes or until mixture is tender. Remove from heat; let cool to room temperature.
In a large bowl, combine apple mixture, ketchup, Jamaican jerk seasoning, salt and black pepper. Add bison; mix well. Shape mixture into six 3/4-inch-thick patties.
Grill patties on a well-oiled grill rack of an uncovered grill directly over medium coals for 14 to 18 minutes or until no longer pink (160°), turning once halfway through grilling. (For a gas grill: Preheat grill. Reduce heat to medium. Place patties on the well-oiled rack over heat. Cover; grill as above.)
Place toast on hot grill during the last 2 to 3 minutes or until lightly browned and toasted on both sides. Brush slices on both sides with melted butter.
Place Texas toast slices on 6 dinner plates. Top with leaf lettuce, burgers and some of the Cantaloupe and Strawberry Relish. Makes 6 burgers.
In a medium bowl, combine chopped cantaloupe, chopped fresh strawberries, finely chopped red onion, finely chopped green sweet pepper,snipped fresh cilantro, snipped fresh mint, finely shredded lemon or lime peel and lemon or lime juice. Toss lightly to coat. Let relish stand at room temperature 30 minutes, stirring occasionally. (Or, cover and store in the refrigerator 4 to 24 hours. Before serving, let relish stand at room temperature about 30 minutes.) Makes about 2 cups.