Re: how do I make my home-made electric generator more efficient?

Your confusion is understandable.  The facts, as presented, are 
confusing.  But, the prime directive in dealing with confusing electrical 
situations is, "Thou shalt believe thy instruments."  They may be the 
cause of the difficulty, but that must be proven.

The key to what is happening is the light bulb.  A generator puts out more 
power by simply twisting its shaft harder.  You are correct in assuming 
that the faster you rotate the wheel, the more work you are doing, and 
since the bulb has no inductance, just pure resistance, its increasing 
brightness with increasing generator speed indicates an increased current 
flow with an accompanying increase in voltage and power.  

But, that only occurs when there is a load [i.e., the light bulb].  An 
unloaded generator only produces enough power to make up for its internal 
losses.  Twisting its shaft harder increases its speed, and product 
increased internal losses.  That may be the key to what you are seeing.

A bicycle type generator uses a permanent magnet for excitation and 
generates AC.   And, permanent magnet excitation in an AC generator is 
subject to complicated shifts in inductance.  If you hook a volt meter 
across the terminals of an unloaded generator, it's possible that the 
voltage indicated can drop from the internal losses as speed is increased, 
particularly in a generator that hasn't been designed for maximum 
efficiency with the knowledge gained by years of experimentation by the 
big manufacturers like English Electric and Westinghouse, etc.

And, if internal losses eat at the voltage, they will also reduce the 
current output, though in an unloaded machine, the current output should 
be zero.  Not knowing the circuit setup for each of the measurements you 
took, it is hard to say.

You might borrow a Wattmeter and use that to determine the power going to 
the light bulb without looking at the behavior of the voltage and the 
amperage.  Of course, it may be hard to find one that can read watts from 
a small generator.  And, you might try a different multimeter to get a 
second opinion on what you are seeing [proof that the problem lies with 
the instrument].

Your original question was about increased generator efficiency. A 
complicated subject that has the general answer that you increase 
generator efficiency by reducing internal losses through both design and 
operation.  In design, reduce resistance losses by using larger wire 
sizes, better electrical and magnetic materials, and heat removal in large 
machines.  And, by controlling induction losses.  That is done in large 
generators by control of excitation - by controlling the power factor.  In 
large power systems, the power factor is really dictated by the load.  

The load in a normal system, being mostly resistance and induction motors, 
has an assumed power factor of 0.8 lagging.  A generator run at a power 
factor of 1.0 would be the most efficient.  It would not have to supply 
reactive amperes to the system.  The circulating current associated with 
reactive amperes, flowing through the generator causes resistance losses 
in the generator, and a decrease in it's efficiency.  

Of course, the other generators in the system would have to pick up the 
reactive load, and the resultant winding losses due to the associated 
circulating current.  Balancing the entire system for peak efficiency is a 
constant challenge to power system operations.