In a medium saucepan, bring 2-3 cups water to a boil. Cook asparagus in the water for 3 minutes, or until crisp tender. Drain and rinse asparagus with cold water, pat dry, and set aside.
Meanwhile, wrap chicken pieces with clear cling wrap, and use a meat tenderizer or rolling pin to pound down the chicken into thin slices. This step will make the chicken easier to roll up.
In a small bowl, combine mayonnaise and honey mustard. Spread 1/2 tablespoon mayonnaise mixture onto each piece of chicken.
Top each piece of chicken with 1 slice of ham, 1 slice of cheese, and 2 asparagus halves. Roll up chicken around the asparagus and wrap with 2 pieces of turkey bacon each.