Buliara could tell by the voe's tone that he was trusting her with the most important person to him in the world, and given that he was a guard himself, and one so respected by Lady Urbosa that even she let him sneak into the city- told him how to outright -so he could stay with the then-princess, she knew that he wouldn't leave her protection to someone else without very good reason.
"The queen will be safe," she promised him, knowing that he was doing her an honor with that trust.