Sometimes there just isn’t a rule for a grammar dilemma. Such is the case with driver side vs. driver’s side.
Either form is quite common and acceptable in writing. Such is the case with other similar constructions, such as dog collar vs. dog’s collar and passenger side vs. passenger’s side.
No doubt the reason driver’s side and passenger’s side sound like they may be wrong is because the word following the apostrophe s begins with an s. To many people, that’s awkward to say aloud. Indeed, a Google search query for the two terms shows that people prefer driver side, which receives about 11 million more returns than driver’s side. Passengers side also is preferred over passenger’s side by 43 million more hits.
Given this, I recommend dropping the apostrophe s or using whatever the stylebook for your publication advises.
My name is Rob Bignell. I’m an affordable, professional editor who runs Inventing Reality Editing Service, which meets the manuscript needs of writers both new and published. I also offer a variety of self-publishing services. During the past decade, I’ve helped more than 300 novelists and nonfiction authors obtain their publishing dreams at reasonable prices. I’m also the author of the 7 Minutes a Day… writing guidebooks, four nonfiction hiking guidebook series, and the literary novel Windmill. Several of my short stories in the literary and science fiction genres also have been published.