Two commenters bring up the following cases regarding the definition of what is public:
What about a Greyhound bus?
Roads are constructed using taxes and thus are "public."
If a Greyhound bus is using said road, is it, in essence, being subsidized by the public?
Here is where I feel the argument about "public" can get expanded to mean just about anything.
I do not necessarily advocate that argument, but the argument does exist.
A more direct example would be a shopping mall that contains a police substation.
The roads are public, but the vehicle is private. Smoking on a bus does no harm whatever to the road or any other vehicle on it. Hence, the vehicle owner has the right to decide on a smoking policy that fits the owner's wishes.
Expanding the definition of public further than this is sophistry, plain and simple, designed to enable people to enforce their will over property they do not own.
Item two. The shopping mall is owned by a private firm, and hence the owner has the right to decide on a smoking policy that fits the owner's wishes. If the police substation is owned by the public, the owners (i.e., the people through their government) have the right to decide on a smoking policy to have in place within that substation. If, however, the substation is owned by the mall owners and leased to the police or given to them free of charge, the mall owner has the right to decide on a smoking policy. Presumably, the owner would accommodate what the police desired, in order to ensure that the substation would remain in operation. But it would be up to the owner—and not anyone else—to decide.
OK, and now on to the next question that will be asked: What if the public, through their representatives, say that they will allow the police substation to operate only if the mall owners institute a particular smoking policy throughout the entire mall? Answer: It will then be up to the owners to decide whether the value of faster police protection outweighs the value of their preferred smoking policy. That will be entirely the owners' call.
I will say, however, that it is utterly dishonorable and wrongheaded of the public to force such a decision on a property owner. Society should provide a public service based on the value of that service to the effort of fostering ordered liberty, creating the highest amount of both liberty and order simultaneously—and on no other consideration. The attempt to constrain liberty (in the form of restrictions on private individuals' property rights) as a tradeoff for the creation of greater order is dishonorable (in that it uses threat of disaster as a means of cowing people into doing others' will) and inimical to the functioning of a free society.
Hence, it is wrong to impose a smoking policy on private buses as a tradeoff for the orderly movement of transportation, and it is wrong to impose a smoking policy on shopping malls as a tradeoff for efficient police protection.