Look for experience with the handling task you need and with dogs who show similar levels of concern. Ask whether lessons are private, online or in the care setting, and how the trainer coordinates with other professionals. A quiet home session may be useful for foundations, while later practice may need a different surface, person or location.
If there is a bite history or serious fear, disclose it before the appointment so the professional can plan safe observation. Ask about muzzle training when relevant, but remember that a muzzle does not make forced practice appropriate. A suitable instructor explains both how risk is managed and how the dog's comfort will guide the pace.