Is it a sin for me if my dog over hears my audio bible?

Um, "dogs" and "pigs" here refers to immoral people, not actual animals. Bear in mind that pigs are considered filthy in Judaism, and that Jewish people are forbidden from eating pig products because of that; those who worked with swine were considered the very dregs of society in those days. Dogs were viewed much the same way, as people didn't keep them around as pets, but they ran loose eating garbage, dung, and anything else they could find (usually after rolling in it). Basically the page is saying "Don't give what is holy to that which is filthy, because it won't be appreciated."