I may not be a fan of atheist memes (or any memes for that matter), but I think there's a great deal of truth to this particular meme. I'm sure that plenty of people have transitioned from Christian to atheist without ever having read any bibles; however, I've also heard from countless ex-Christian atheists that this was an important part of their own path to atheism. I think I would have left Christianity behind sooner or later even if I never looked at their bibles. Doing so probably sped up the process though.
Growing up, I was frequently told that the bible was "holy" and that it was the greatest book ever written. Needless to say, that made me quite eager to read it. When I was given my first bible, it was kind of a big deal. Finally, I'd get to see what all the fuss was about. To say it was disappointing on that initial read was an understatement. Even as an early teen, the contradictions and inconsistencies were apparent. But the cruelty of the genocidal "god" and the manner in which it interacted with humans were among the things I remember most. I finally understood what "god-fearing" meant, but I was puzzled as to why this thing deserved to be worshiped.
I have heard many atheists who were former Christians describe similar experiences. This is one of the reasons I've always found it puzzling when Christians try to drum up fears about atheists attempting to "ban the bible." I'm not sure I've ever encountered an atheist who didn't think that more people should read this book in order to discover what it actually says. Most of us seem to agree that we'd have more atheists if more people were to do so.
Is the road to atheism really littered with bibles? I'd say so. Discovering for oneself that "the good book" is anything but good has a way of prompting questions and stimulating critical thinking. Learning how little relevance it has for modern life has a similar impact. The process probably isn't instantaneous, but it certainly helps to get the ball rolling. At least, I found that it had that effect.
In any case, making it more difficult for people to get their hands on a bible is one of the last things I'd ever want to do. We need more atheists. The more people who discover what is in these various "holy" books, the better. By doing so, I think it becomes far more difficult to claim that anything about them is holy.