After researching and trying both routes, we figured out that you can either take Ocean Parkway or Bedford Ave. Ocean Parkway has a pleasant separated bike lane, which is better for conversational biking, but adds two miles to the ride. If you take Ocean Parkway, turn left onto Neptune Ave before you reach the boardwalk, which turns into Emmons Ave. If you take Bedford Ave, you take a left right onto Emmons Ave. Either way, when you reach the intersection of Brigham and Emmons, you will see a path set off to the right of the ramp onto the Belt Parkway (pictured below).
You want to take this bike path (not the ramp onto the highway), which follows the wetlands along the shore and takes you right to Flatbush Ave and over the bridge to the Rockaways. We passed an area where Hurricane Irene had washed away the path, despite the bags of sand buffering the coast - no matter, just walk your bike through the sand at this spot and enjoy the view.
Once you're over the bridge, make an awkward left just before all the field and parking lot business, and then turn right just before the beach and follow the path through the woods until you reach at least post 22 (which also has a bike rack) in order to hit the lawless Fort Tilden beach, rather than Jacob Riis. It's not the most straightforward journey, which is why I thought it would be helpful to put these directions on the internet.