They got their wish, although only in the sense that they watched them field all day as Hampshire scored 281-4 after being asked to bat.
Root and Bairstow were made to wait for their first innings of the season as Yorkshire exercised the right of the visiting side to bowl.
It was a decision based on the overhead conditions, although the hay-coloured pitch proved a good one for batting with barely a hint of green on display.
Instead of Root and Bairstow making hay, it was a man who has fallen out of England favour who kept the scoreboard operators busy.
Hampshire’s James Vince had not scored a first-class hundred since an innings of 119 against Yorkshire at Headingley in April last year.
But he enjoys batting against the White Rose, against whom his 143 yesterday was his third century against them in the Championship, to go with two fifties.
It helped to put his team into a good position and left his opposite number, Gary Ballance, seeking a strong start to day two.
“If we can get a couple of early wickets, I think that we can put them under pressure with the second new ball,” said the Yorkshire captain.
“I thought we bowled quite well for the first two sessions, but we just let it get away from us in the final session.
“We knew that it was going to be quite a good wicket, but we just thought with the overhead conditions as they were that the ball might swing around.
“It did swing around a bit, and we put them under pressure early on, but we couldn’t sustain it for the whole day.”
With Root and Bairstow back in situ, after England had told them to rest for the opening two rounds, Yorkshire were in the rare position of being at maximum batting strength.
They should certainly enjoy batting when they do get the chance, for the pitch has not offered much to spinner or seamer, although there was a bit there with the new ball, as is invariably the case.
For the most part, though, the best that Yorkshire could do was to plug away and try to stifle the scoring.
They did it to the extent that the cricket was mainly attritional, enlivened by the occasional flourishing boundary from Vince, who hit 20 of them in an innings that comprised 233 balls.
Before a 1,500 crowd, who watched in weather that was almost warm enough to dispense with a coat, Yorkshire began impressively against a side who beat them by four wickets in the reverse fixture at Headingley earlier this month.
Ben Coad built on his status as the country’s leading wicket-taker by having Michael Carberry caught behind off a flashing drive outside off stump, Bairstow effecting a smart take as he tumbled to his left.
But from 9-1 in the sixth over, Hampshire rallied to reach 75-1 at lunch, by which time Vince had 39 and opener Jimmy Adams 29 for his morning’s endeavours.
Adams perished to the first ball after the interval, Coad pinning him lbw pushing forward, but Yorkshire missed a chance to get rid of Vince in the next over, Adam Lyth failing to hold an edge at second slip off David Willey.
Vince advanced to a 109-ball half-century by pulling Coad for his eighth boundary, and he found a firm ally in 21-year-old left-hander Tom Alsop, with whom he added 82 in 27 overs.
So well did the pair perform that it was something of a surprise when Alsop was trapped lbw by Steve Patterson for 40, attempting to work through mid-wicket without any foot movement.
Vince, 26, made his Test debut against Sri Lanka at Headingley last year, but managed only 212 runs in seven games before the axe fell.
The reasons why he was called up in the first place, however, were in glorious evidence as he defended solidly and attacked stylishly.
The elegant right-hander went into tea on 97 and reached his 19th first-class century from the fourth ball after the break, cutting Root to the boundary.
Vince reached the milestone from 180 balls, coincidentally his score when he registered his maiden first-class hundred, against Yorkshire at Scarborough in 2010.
Towards day’s end, as the murk descended and the banks of trees behind the pavilion became a sweeping mass of black, the action proceeded beneath floodlights.
With 16 overs left, umpires Billy Taylor and Alex Wharf decided that it was too dangerous to allow Yorkshire to take the second new ball, and so the players went off for bad light.
The delay was brief, Coad taking his third wicket when Sean Ervine was smartly caught by Bairstow, low to his left, ending a stand of 110 with Vince in 26 overs.
But conditions deteriorated again and 10.3 overs were left unbowled when the final curtain fell at 6.25pm.