One of the best ways to keep your gums from bleeding when you come in for a cleaning is to floss regularly. Brushing your teeth before or after flossing is less important than whether you floss or not.
Of course, impressing us with gums that don't bleed isn't really the point. Bleeding can indicate a need for improved gum maintenance and oral health habits. And if you are still smoking, quit now. Smoking causes gum disease, bone loss and oral cancer.