Why is the swelling of bread when placed in water not considered to be caused by osmosis?
The phenomena that you are describing, where bread, which is a porous material, similar to a sponge, absorbs water, is the absorption of water by capillary action. 

As @Joel mentioned, osmosis is specifically the flow of a fluid across a semipermeable membrane, such as the plasma membrane of a cell or dialysis tubing, that occurs in such a way as to cause a flow from an area of low concentration to an area of high concentration. This flow eventually leads to a state of equilibrium when the concentration on both sides of the membrane is the same.

The wikipedia article on Osmosis gives this definition:


  Osmosis is the spontaneous net movement of solvent molecules through a semi-permeable membrane into a region of higher solute concentration, in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a semipermeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations. Osmosis can be made to do work.
  - Wikipedia: Osmosis



- By OpenStax College [CC BY 3.0 (http://creativecommons.org/licenses/by/3.0)], via Wikimedia Commons

The bread is not selectively permeable, and it will continue to absorb liquid until it is fully saturated. This isn't actually an equilibrium, because additional water would do nothing to change the concentration on one side of the bread or the other. If you added more water to one side of a semipermeable membrane in equilibrium, by Le Chatelier's principle, you are will force the reaction (in this case, you change the concentration) to one side, then the liquid would again flow from the area of low concentration to the area of high concentration.

Capillary action is the result of water flowing into the small spaces, such as the air bubble that form in bread when it bakes, in the absence of a force "pushing" it into those spaces, or against the force of gravity. The liquid accomplishes this through intermolecular forces that cause adhesion of the molecule to the surface of the material that is absorbing it and cohesion of the molecules in the liquid keep them associated to one another, and as the liquid moves into the spaces, it is able to pull the other liquid molecules along into the space.