It sure can be hard to get a diagnosis with a sputum culture, but most docs are right to hesitate on doing a bronchoscopy - these are definitely not without risk, especially in someone who has already had hemoptysis (coughing up blood.)
Has anyone ever talked about doing an induced sputum culture? Under the supervision of a respiratory therapist or assistant, you use a nebulizer to inhale 10% (hypertonic) saline solution, which typically induces coughing and brings up sputum.