Whither property rights
Regarding the constitution though...
The 3rd, 4th and 5th amendments all touch on property rights.
3: no military quartering in time of peace without consent.
4: no unreasonable search and seizure (the right to be secure in their persons, houses, papers, and effects...)
5: No person shall... "be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation."
This last one is especially pertinent to the smoking initiative because private property in this case is being treated like public property. In fact, I have heard that very language. They are calling the businesses in question "public," which is legal absurdity.
There is a similar (although more extreme case) where some courts have declared shopping malls part of the "public square," forcing the owners to give space to political speech on their property. The arguments for this are varied and it depends on the state usually. Some say that malls are replacing the public arena (the street sidewalk) and therefore must give space for the otherwise available public speech.
Regardless, a smoking bar is still private property, and while there isn't a legal expectation of privacy, like in a residence, the question of who can do what on the premises is still in the hands of the owner.