[Alcuin]

I think that before the White Council meeting in III 2851, Saruman may already have begun to smoke. I cannot prove that, but it is a mark of smokers temporarily deprived of tobacco that they become extremely irritable when another nearby is using it freely (you may take that as fact from one fond of tobacco), and I think this explains Saruman’s tremendous irritation with Gandalf, who was “smoking prodigiously” (probably because he was irritated with Saruman, and told Frodo and his friends (Unfinished Tales, “Quest for Erebor”) in Minas Tirith after the War of the Ring,

‘I was very troubled at that time … for Saruman was hindering all my plans.’

Now, that is a little out of the timeline, since Gandalf met Thorin at Bree in III 2941, ninety years later, but I think he was already thoroughly frustrated with Saruman’s intransigence in acting against Sauron in III 2851, which he displayed in the affair of grabbing at the smoke-rings, whatever other subconscious motivations may have driven him to do that.

In the essay “The Istari” (op. cit.), there is a passage that says that

Saruman had long taken an interest in the Shire – because Gandalf did, and be was suspicious of him; and because (again in secret imitation of Gandalf) he had taken to the ‘Halflings’ leaf,’ and needed supplies, but in pride (having once scoffed at Gandalf’s use of the weed) kept this as secret as he could. Latterly other motives were added. He liked to extend his power, especially into Gandalf’s province, and he found that the money he could provide for the purchase of ‘leaf’ was giving him power, and was corrupting some of the Hobbits... [footnote 17 here remarks on Farmer Cotton’s observations concerning Pimple’s purchases of leaf-plantations] … He … began to collect detailed information about the Shire… When Gandalf had refused to treat with him Saruman redoubled his efforts. The Rangers were suspicious, but ... Saruman was still recognized as an ally.

Now that passage clearly refers to the period immediately before Frodo’s departure, and is followed without interruption by a description of the Nazgûl capturing and suborning Saruman’s spy, the “squint-eyed Southerner” the hobbits saw in The Prancing Pony, placing this particular period in the summer of III 3118; however, Saruman’s influence was already well-established by then.

A little further in this essay is a section labeled “(iii) Concerning Gandalf, Saruman and the Shire”, in which it is said that

Seeing then that Gandalf thought the Shire worth visiting, Saruman himself visited it, but disguised and in utmost secrecy...

Yet in truth Saruman’s spying and great secrecy had not in the beginning any evil purpose, but was no more than a folly born of pride. ... observing Gandalf’s love of the herb that he called ‘pipeweed’ ..., Saruman had affected to scoff at it, but in private he made trial of it, and soon began to use it; ... it came to [Saruman’s] knowledge that he had not been all unobserved by the keen-eyed Halflings, and some ... had mistaken him for Gandalf.

The words “Saruman had affected to scoff at it, but in private he made trial of it” would seem to indicate that Saruman’s initial use of pipeweed followed the White Council meeting of III 2851: the passage describing Gandalf’s grabbing the smoke-rings is preceded with the words

It was at the great Council held in 2851 that the ‘Halflings’ leaf’ was first spoken of…

which might indicate that it was only after event this that Saruman began his diversions. I believe Saruman must already have begun his experimentation with tobacco, in part because of his exceptionally harsh reaction to Gandalf, the kind a deprived smoker would show.

Gandalf’s especial interest in the Shire began after the Long Winter of III 2758, in which many of the hobbits died, and Gandalf came to their aid. In “Quest for Erebor”, he said he was impressed by

their courage, and their pity one for another. It was by their pity as much as by their tough uncomplaining courage that they survived.

The following year, III 2759, was when Saruman took up residence in Orthanc with the permission of Beren, Ruling Steward of Gondor. Saruman’s purposes even then were no longer pure: he was motivated by his “study of the records of Gondor [and his] interest [in] the palantíri and the possible uses of those that survived” (Unfinished Tales, “The Palantíri”), presumably to search for the One Ring.

Since we do not know when Gandalf began to smoke, it is difficult to determine when Saruman began. Tobold “Old Toby” Hornblower was credited with being the first hobbit to smoke: that would have been around SR 1070 (III 2670 - RotK, “Appendix B” ): Gandalf could not reasonably have begun before then. Saruman’s interest in pipeweed is unlikley to predate 2759; it certainly began soon after the White Council meeting of 2851, if not before (I still think his reaction to Gandalf’s smoking was extremely harsh: he sounds like modern, real-world anti-smoking zealots, often former smokers themselves); and before the War of the Ring in III 3118, his habit and the influence it gave him in the Shire was well-established, possibly even when the Sackville-Bagginses had Bilbo declared dead in 2942 so that they could take possession of Bag End.