Agreed- the bike lane planning where Delancey hits the Wburg bridge is not so great, or intuitive, or marked so well.

Here is my answer in a few parts:

A]] You would be able to bike straight on if the D.O.T. built a bike lane that ran with the flow of traffic, which would be more intuitive.
Instead, all paths require you to physically turn your bike at a right angle before continuing on. This binds you to the perpendicular street’s traffic lights and not Delancey’s. You’re technically making a right turn then a left turn to get onto Delancey.

You should be able to turn onto Clinton or Suffolk without stopping if the light is green. You can continue onto Delancey if the light is green as well because you’re more or less making a technical left turn. In NYC turning on a red light is prohibited; so because the bike lane puts you at a right angle to Delancey- if cars on Delancey are going, bikes should be stopping. If nobody’s watching, I imagine you could try and merge with Delancey, but it is kinda risky with the crazy speeding drivers coming off and on the bridge.

B]] The Clinton St bike lanes to your left or right when getting off the bridge are meant to deter you from going straight. Grand St runs the same length as Delancey and has much lower car traffic (cutting off near Bowery), and Houston cuts to the other side of the city.

The bike lane that does allow you to go straight is geared at bicyclists coming down Suffolk St to get on the bridge. But if the Suffolk light is green you can use that to turn onto Delancey.

However, if you’re doing the reverse and biking down Delancey to get onto the Williamsburg Bridge, you can get on at any time with no problem.

Those are my more technical answers, keeping in mind that cops started cracking down and ticketing bicyclists this Spring. Biking in the city is hardly the friendliest, but until things get sorted out (which will be years).. if a cop’s in sight, probably better safe than ticketed.

Best of luck!