Moral principles are all about what legislation is about. The Bible is one source of inspiration. That is what the founders thought, and that is true to this day. Trying to corral the founders into the debate about the role of religion in the public square today, won't get one far. The founders thought that the voters should enact wise legislation, and good moral character was essential to that, and should be fostered. That is my take. The game of capturing George Washington or Ben Franklin or Thomas Jefferson, of James Madison, who each had their own take about religion, although not all that different, and all would be amazed about the religious fervor of some today, vis a vis the public square, into today's religious boxes, is errant.
Looking at the society in which the Founders and their immediate descendants lived, it was far more formally Christian than is contemporary America. Churches were the primary educators of the young, with virtually all colleges having religious origins. Many states had test oaths for public office that forbade atheists, and in some cases non-Christians, from holding public office. Until the early 20th Century, blasphemy was a crime, divorce was only granted in cases of adultery or desertion, and sexual relations outside of marriage were prohibited, as were abortion, birth control, and pornography. Such prohibitions were established in English common law and remained in force until the last century.
It is worthy to note that none of the Founders, even heterodox ones like Franklin and Jefferson, never lobbied to overturn these laws, for even if they may have rejected the miracles in the Bible, they accepted at least the utility of the moral code therein. For example, Jefferson authored a bill that would have made castration the punishment for sodomy. Virginia's punishment, though harsh, was less than the death penalty imposed by Connecticut, South Carolina, Vermont, and New York for the same crime.
The secularization of American society and the cordon sanitaire between government and Biblical principles that currently exists are ahistorical and have no roots in the writings of the Founders, irrespective of their personal religious beliefs. Rather, it has its roots from several sources, such as the legal positivism derived from philosophers such as William James, the Social Gospel movement in liberal Protestantism and its corollary in liberal Catholic social thought, the cultural Marxism deriving from the Frankfurt School in which the New Left is rooted, and deconstructionism common to postmodernism.
If you wonder how this nation has gotten to the point where perverts are welcome to Easter egg hunts, do not look to Jefferson, Madison, Hamilton, etc., and their philosophical forbears like Locke, Blackstone, and Montesquieu. Look rather to John Dewey, William James, Oliver Wendell Holmes, Earl Warren, Alfred Kinsey, Herbert Marcuse, and Jacques Derrida.