We do have bike lanes. A lot of them in fact - though some of them are still pretty scary. I rode a Citibike up 6th Ave in the bike lane in the middle of the afternoon yesterday and it was a little hair-raising.
One of the very cool things about this program is that all the bikes are equipped with GPSes, and combined with the data from the docking stations themselves, there's a stated intent to use this data to determine where more bike lanes and bike lane improvements will go in.
Don't worry, bike lanes in the Netherlands can be scary too, ;). Especially if you're a tourist and compete with natives that will go faster. Perhaps even moreso on a wintry day when it's slippery.
Ah, it's not the bikes in this case, but rather that you're riding in a painted lane on a road occupied by a sea of extremely aggressive cab drivers ;)
Some roads have protected bike lanes where you're separated by traffic via a concrete divider, potted plants, or parking spaces, and those definitely feel a lot less scary.