May I suggest a different and I believe safer and easier way to the Manhattan Bridge for you which is on bike lanes. I agree with the other posters that you should take Ocean Parkway up and into Prospect Park. Once in the park head north and exit the park at Grand Army Plaza right after the "hill". At Grand Army Plaza follow the bike path across Flatbush and on to Plaza Street and then make a left from Plaza on to Vanderbilt. Stay on Vanderbilt up to DeKalb Avenue, where you make a left. Take Dekalb to Ashland Place which becomes Navy Street. Stay on Navy Street until Sands Street where you make a left on to a very nice separated bike path, which leads you to the Manhattan Bridge bike path.

Good luck and trust me the riding will become easier very quickly.