You can also try Woodstock from 90th to 28th, no bike lane from 52nd to 42nd, but very friendly to cycles. Take 28th to Gladstone, jog to 26th and take 26th to Clinton, than Clinton to 20th and than take ladds addition to 12th. At which point you'll have two routes to the bridge.
As a commuter I have been using this route for a year now with no problems.
Just another option for you to consider.