Simply put, bias-free language means that you don't exclude members of the population. This means that you never use only masculine pronouns or adjectives (he, him, or his) to refer to persons when gender is unspecified, because you're excluding approximately half of the population. On the flip side, using only the feminine pronouns (she, hers, or her) will exclude the other half.
Using bias-free language and avoiding sexist terms doesn't mean you need to re-create the language to accommodate the prevailing “political correctness” of the day. Herstory may have its place in humorous, informal writing, but it's out of place in formal writing, regardless of the sex of the person making that history. Shortcuts like s/he may be fine in your personal notes or even in some informal writing, but these kinds of shortcuts have no place in formal usage.
One of the common mistakes beginning writers make is to use what is perceived as “gender-neutral” language. So, they use words like they, them, or their to create an inoffensive catchall that can count for everybody. This works great in theory, but grammatically, it's wrong.
Some publishers choose to overcome this challenge by alternating forms. In one passage, the word him will be used, and in the next passage, the word her; alternating, then, is simply for the sake of illustration. Often, a note will appear somewhere toward the front of the book stating that this is the publisher's objective to obtain a gender-neutral, all-inclusive message. This is merely one way of doing it.
There is another way, and it has been done for many, many years. If you want to be gender inclusive, just use both:
Once we select the correct candidate, we will have him or her fill out the proper tax forms before beginning employment. If he or she wishes, the forms can be completed on the first day of employment, rather than beforehand.
The use of he or she tends to be relatively invisible. If you overuse it, it may look a little clunky, but you can become quickly adept at restructuring sentences so that you're using the words appropriately. Never use they when you mean he or she, and never use them when you mean him or her. Not only is it grammatically incorrect, but it can also add ambiguity to your sentence, because people may have to start trying to figure out who you're talking about.