For greater influence on the biceps you might start with the close curl grip chin, immediately followed by the BB curl. Feel free to cheat a bit on the curl. Cheating, with control (not to the point of reverse cleaning the bar) can be very rewarding for most. This form of SS'ing can be a mass builder. Heavy BB curls can give the advantage of building size rather quickly but other DB exercise do have their place in any arm program. The incline DB curl is another builder that comes to mind.
One of the few BB curling movement that seems to affect the biceps more directly is when bending over at the waist, almost to a 90 degree angle. The bar should be hanging freely at the starting position and than curl the bar up to the face area. Keep the elbows out and away from the body throughout the full motion of the exercise. Can get a favorable muscle cramp, hitting the biceps from a total different angle.
An EZ bar allows less strain on the wrist and forearms for a lot of people. But, to me, it's more like six of one and half a dozen of the other. Another EZ bar exercise that also works well is to position the hands wide, medium and close grip (6") and curl two set's in each position. Attacks the biceps from different angles . The reverse BB curl, either straight or EZ bar is a fine exercise also. Good Luck.