The nice and easy way, half of it on bike lanes, starting off on your original street of choice:

President -> 5th Ave -> Bergen -> Smith which turns into Jay -> bridge.

The only hot spots are around the bridge entrance. Merging with the off ramp traffic can seem dicey, but keep a sharp eye, enter into the right lane smoothly, and you're there. Alternately you can cut across Tillary and hit the Brooklyn Bridge.

No speeding cars, no fuss, no muss.