Which of the following is a common method of direct contact transmission?

The correct choice is shaking hands, as it exemplifies direct contact transmission, which occurs when one person physically comes into contact with another person or an object that has been contaminated by infectious agents. This method facilitates the transfer of pathogens through skin-to-skin contact, making it a key example of how infections can spread among individuals in close proximity.

Other forms of contact mentioned, such as sharing water bottles, can also facilitate transmission, particularly if the bottle is contaminated, but they do not strictly categorize under direct contact in the same immediate manner as shaking hands does. Breathing the same air refers to airborne transmission, which involves inhaling infectious particles suspended in the air rather than physical contact. Using public transportation may increase exposure to infectious agents, but it does not inherently involve direct physical contact like shaking hands does.