It's my impression that nowadays, conservatives usually assume the original Bill of Rights applies to Americans in general. It applies at the level of state and local government, and to some degree, even in the private sector. But I've also seen it claimed that that's anachronistic. Rather, that's due to the "incorporation" doctrine whereby some provisions in the Bill of Rights were reapplied to the states via the due process clause. Hence, that doesn't reflect original intent.
However, I think that's questionable. From what I've read, Enlightenment political theorists had a doctrine of natural rights. Indeed, we see an example of this in The Declaration of Independence: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
To some degree, natural rights were distinguished from political rights. Natural rights were universal whereas political rights were individual. In modern jargon, we might recast the distinction in terms of human rights and civil rights, where human rights are innate and universal while civil rights are conferred by gov't.
However, the distinction isn't that cut-and-dried, from some political rights were viewed as derivative natural rights. The function of some political rights was to safeguard natural rights, viz. freedom from oppression.
This seems to be the basic relationship between The Declaration of Independence and the original Bill of Rights. Although a few provisions in the Bill of Rights might be merely individual rights, in the main they appear to be derivative natural rights. In other words, they are specific political provisions to safeguard natural rights. Insofar as that's the case, it's not anachronistic to view the Bill of Rights as an extension and application of natural rights to the political sphere. In that event, the Bill of Rights is not confined to the Federal gov't. In some cases, it's not even confined to the public sector.