Most interfaces, to both computer and RealWorld devices, are designed with the presumption that the user is right-handed. For the most part, about 80-90% of the time, this assumption is correct. For the other 10-20%, life gets frustrating.
Since a computer can dynamically change its interface to suit the user's needs, it is possible to avoid DominantHandBias by being dominant hand customizable. Mostly, this involves placing widgets on the mirror side of the window.
As a handy bonus, a completely internationalized application--one that supports BiDi--must also have this capability, called GUI mirroring.
People also have a dominant leg. You can see how there is also a dominant leg bias. Consider the location of a car's pedals, or even snowboarding where there is a distinction between "normal" (right-legged) and "goofy foot" (left-legged).
Just an anecdote about hand bias:
I play guitar, and at the beginning, it struck me that the more complex hand movements, what you would expect to be done with the dominant hand, the fretting, was done with the non-dominant hand. I have tried flipping it over on occasions, and I can now sort of do it, but it has never felt right. --DaveJacoby
I thought about this too, and find myself at peace with the conclusion that carefully, but in tempo and with feeling, aiming the plectrum at the strings requires more dexterity then holding the notes and chords with the non-dominant hand. Finding the right position and holding it (plus needed force to keep the string down to the fret) takes some effort, and excercise and training to get it right, but is less intensive work than striking the correct string with the correct force in the correct direction at the correct moment (as when building rhythm). -- StijnSanders
The same is true of string instruments such as the violin.