I heard this mentioned somewhere. Have also seen laws in some of the colonies that were almost verbatim taken from the Bible, however I can't find any mention of a particular state requiring (or even just highly encouraged) someone aspiring to practice law to know the Bible?
This is unlikely.
Knowledge of the Bible was commonplace among literate people in the early U.S., and literacy rates in New England and the Mid-Atlantic States (and the colonies that preceded them, and later on in the Midwest) were among the highest in the world - with literacy being reserved for the merchant and higher classes in many parts of the "Old World".
Literacy was much less widespread, however, in the American South or Appalachia, which were also among the most secular parts of the United States prior to the Second Great Awakening around the 1830s to 1840s, when the American South transformed itself into the most religious part of the United States.
Particularly in areas were literacy was lower, litigation was much more common than it is now over matters which we would consider petty, but most legal proceedings were similar to modern, lawyerless small claims court (and courts often ventured into activities that we would no longer consider to be legal as opposed to governmental administrative matters today like road improvements and welfare payments).
The privilege of representing someone else in legal proceedings was vested in individual courts or judges but granted liberally, to pretty much anyone who was literate and had some familiarity with legal texts.
The legal profession only began to be formally regulated as such in the late 1800s with the first law schools providing a significant share of the bar starting around the 1870s (before which most lawyers started out "reading law" as an apprentice in another lawyer's office).
Admission to the practice of law, which has handled separately by each particular court until then, not on a uniform statewide basis, did not require any particular formal education at the time although literacy and access to law books was a practical necessity. It was not very regularized or bureaucratic. Often a referral from an existing lawyer was the main qualification and admission to the federal court bars for lawyers already admitted to practice in state courts still works that way today.
So, it is highly unlikely that any particular state required (or even just highly encouraged) someone aspiring to practice law to know the Bible, to an extent more than this was encouraged for every literate adult.
As additional context, the primary qualification for admission to institutions of higher education up until the late 1800s was not knowledge of the Bible, but a sound foundation in reading, writing and speaking Latin and Ancient Greek, a skill set which had both religious and secular applications.
In the time period prior to the late 1800s, higher education mostly prepared young men for in the U.S. and in the North American colonies, either to be a member of the clergy (a track that naturally enough usually excluded most future lawyers), or to be a "man of letters" which primarily involved studying the classics, philosophy, rhetoric, history, and other humanities. Formal instruction in science, to the extent it happened, was taught as a subfield of philosophy (natural philosophy) or in connection to astronomy or math which were recognized as major academic disciplines in the early modern era in Europe.
College educated "men of letters", who often went on to practice law (although as many or more sought other careers in fields such as politics, diplomacy, civil service, and business), were probably more knowledgeable of Greco-Roman mythology, and classical works of history, philosophy and rhetoric, than they were especially knowledgeable about the Bible or theology. As the term suggests, these avocations were not necessarily seen as completely distinct careers. Instead, they were more akin to different specialities within the Uber-category of work done by college educated men.
Notwithstanding the Establishment Clause of the First Amendment, there were parts of the United States, mostly in New England, where government established churches continued in existence after the adoption of the 1791 Bill of Rights (which initially applied only to the federal government). But this had ceased to be the case a decade or two before the U.S. Civil War. By the time that the legal profession began to be systemically regulated, the divide between church and state was well established. So it is unlikely that Biblical knowledge would have been a formal, or even highly encouraged, requirement for the practice of law.
My suspicion is that the statements you heard were the product of an educational movement, particularly common for religious home schooling, that has tried to claim, inaccurately, that the United States was a "Christian nation". This movement often distorts historical reality in an effort to prove that point.