Brooklyn bars hire on personality and reliability first, resume second. Most openings never get posted -- they are filled by whoever walked in at the right time -- so treating the search as an in-person activity beats sending email.
Go in person, between 2pm and 5pm. That is the dead hour between the lunch rush and the dinner shift, and it is the only time a manager has ten minutes to talk. Never ask about a job on a Friday or Saturday night. Bring a short printed resume even if nobody asks for one.
Get your certifications before you start looking. New York does not require a bartending license, but most bars want you alcohol-training certified, and anywhere serving food will expect a food handler's certificate. Having both in hand removes the easiest reason to pass on you.
Be honest about experience, because it shows up immediately on a busy night. If you have never worked a high-volume bar, say so and apply for barback roles. Barbacking is the normal way into Brooklyn bartending, it pays while you learn the well, and good barbacks get moved up within a few months.
Know the neighborhood you are applying in. A cocktail bar in Cobble Hill, a dive in Bushwick and a brewery in Greenpoint want different things from the same job title. Have a drink there once before you ask to work there, and mention that you did.