I take Vanderbilt to Flushing Ave at the end, and then Navy and the bike lane to the Manhattan Bridge. It is bike route the entire way, although Vanderbilt only has a bike lane to Fulton and then is a "shared" roadway. There still isn't that much traffic to deal with.

The problem is the Manhattan Bridge leaves you on the east side. That's OK for me as I work at 2nd Ave, but to get to the UWS you've got to cut across. At least one crosstown street is marked somewhere south of Houston.