5 minutes from the Bowery to the West Side Hwy, is not fierce it's crazy. In that type of traffic I doubt if I could make Broadway in 5 minutes let alone the West Side Hwy.
Your currently using almost all the streets I can think of to the Bridge without going completely out of the way. As to the West Side Hwy, try cutting up West Broadway or Centre Street, if you like the frantic pace, those are two streets which can provide it.