lulu, if you look into this, you will learn that all tours on the site MUST be conducted only by employees of the Auschwitz management. The product "Auschwitz tour" consists of how you get between Krakow and the two camps, and what your experience is on the journey.
Some people with rock bottom budgets use public transportation. Others hire a car and driver for a private trip (let's say, 1.5 hours) between their hotel and Auschwitz. In fact, the trip between Auschwitz and Birkenau is usually done on the proprietary shuttle bus, because the camp guide takes you there and says he/she will meet you at Birkenau, after the first, longer part of your (say) 3-hour tour. Even if you have a car and driver, the driver usually picks you up at Birkenau, after the second segment of the official tour.
My report is no better than anybody else's, but here it it:
Edit: "Auschwitz tour" product also includes the issue of whether they get you the official, timed entry tickets, or whether you get them yourself, online. It may or may not be that some executive-tour providers may have tickets for sold-out days. I have no actual data on that.
Just like other high-demand places (like the Anne Frank House or The Last Supper or The Statue of Liberty), the actual tickets are impossible to get on short notice for many months of the year.