Here’s Joel McDurmon answering that question, and assigning some reading.

Well, that first of all depends on how one defines “Puritan.” It also depends on exactly what you mean by “that view” of Theonomy, because both Rush and Bahnsen 1) did not fully agree with each other, and 2) left many exegetical questions vague or unanswered, which means other people (“Puritans” included) could disagree with either or both at various points as well.

Nevertheless, there is substantial agreement, in some cases almost total with Bahnsen, among some of the Westminster Divines, some of their precursors, and some of the New England Puritans.

For their primary sources, I would start with these few places:

Johannes Piscator, Disputations on the Judicial Laws of Moses.
https://americanvision.org/12386/new-piscator-on-the-judicial-laws-of-moses-1607-or-theonomy-before-theonomy-was-cool/

Disputations on the Judicial Laws of Moses
The appendix in this book lists several theologians who followed this view, which is almost identical to modern biblical Theonomy.

For New England examples, see this collection of three sermons which relate that very view, clearly influenced by Piscator, et al after him. Appleton’s sermon especially is dead-on.
https://americanvision.org/12034/gods-law-in-the-american-founding-another-brand-new-book-from-american-vision/

https://store.americanvision.org/products/gods-law-and-government-in-america

Finally, there is a terrific historical essay in a journal called The Confessional Presbyterian. The essay is on “The Westminster Assembly and the Judicial Law: Part One, Chronology.” It outlines many published views of the Divines. Some are dead-on for Bahnsen’s view. Other’s are Constantinian. Some are in between. Still others are completely dismissive of the judicial laws. There was a full spectrum of views at the assembly. I recommend this essay, but the companion essay right after it, “Part Two: Analysis” is awful.

These all should give you a great start on this question and some primary sources. There are more listed in that last essay. It may be good at some point to pull them up a reprint them, but Piscator and the New England sermons are all I have in full right now.