Does moving something horizontally in gravity do no work? 
Bill’s job is to lift bags of flour and place them in the back of a
  truck, which is parked next to him. Sally is loading the same bags of
  flour into a similar truck that is located 10 m away. Sally wants a
  raise because she says she is doing more work than Bill. Does the
  physics definition of work support her claim?

Attempt: By the definition Work is Force multiplied by the Displacement in the direction of the force. Sally does the same amount of Work when she lifts the bag. But, when she cares the bag for 10 m to the truck there is no force exerted on the bag in the direction of the truck. Therefore, she does the same amount of Work. Is my reasoning correct? Why the Force exerted in the direction of the truck is zero?
 A: Yes, your reasoning is correct.
You could also reason this way: the work done by Bill and Sally is turned into energy.  In both cases the final energy - potential energy of the bag - is same for both of them.
Edit: after editing, you also asked: "Why the force exerted in the direction of truck equals zero?"
Let's start with a reasonable assumption that bag is carried toward the truck with the constant velocity.  In case of constant velocity, according to 1st Newton law, the net forces equals zero.  There are only two forces acting on the bag: the force of gravity (vertically down), and the force of Sally (vertically up).  Therefore there is no horizontal force in direction of the truck.
A: Sally is correct. Of course they both do the same amount of work lifting the bag, but Sally does additional work moving the bag to the truck. This is because the bag had an initial horizontal velocity of zero. It is not possible to move something at a constant velocity that has in initial velocity of zero. First it will be necessary to accellerate it for some time and distance. Since the object being accellerated has mass, force must be exerted. And since the force must be exerted over some distance, however small, work has been done.
