The use of bicycles for riding--to enhance infantry speed and carrying ability--seems to have been hit pretty well.
But, one thing that hasn't been covered is the use of bicycles strictly to increase the load carried. A person walking beside a reinforced bike (there are also ways to add the ability to pull the bike from in front or pull it from behind, which can make things easier) can move at a fairly normal pace while loading the bike with 3-400 lbs (~140-180 kg) of equipment and supplies.
That technique has been used often by less mechanized armies, such as North Vietnamese/Viet Cong. It's pretty darned effective and actually outperforms a single mule. Of course, one person could lead multiple mules and only handle one bicycle, so that may even out. But, mules have to be fed...a lot.
Bicycles do need maintenance, but so do strings of mules.
Of course, if the terrain is steep or very rough it might take two or more people to get such a laden bicycle up a hill or across a stream...but that's something that can be worked out. (Even to the point of carrying a Come-a-long to help out--but it still takes a couple people.
http://en.wikipedia.org/wiki/Comealo...n_or_wire_rope)
It doesn't take much to realize that a bicycle could add a whole lot of ammo, grenades, mines, etc. to an individual soldier's arsenal. Not to mention plenty of water and MREs.