The first truck grabs the paper/cardboard boxes. These should not be bagged. The second truck grabs the rest. I have seen lots of people put their recycling in bags, even though the website says not to. Maybe it depends on the type of bag? Blue/clear? Whatever the case, I would first separate your recycling into paper/cardboard, and then plastic/aluminum/glass. I use a cardboard box for my cardboard, and my blue bin for the rest, unbagged.

https://www.jerseycitynj.gov/cityhall/dpw/recycle

ETA: make sure your bin is visible from the street! Our recycling was missed one time because it was not visible because of parked cars. I try to move it to a place seen from the street between parked cars or by light poles.