Root and Bairstow have not been made available by England for the games against Hampshire at Headingley (April 7-10) and Warwickshire at Edgbaston (April 14-17), while Adil Rashid is also unavailable for the Hampshire match.
Root and Bairstow are available for the third Championship game, against Hampshire at Southampton (April 21-24), followed by a handful of fixtures in the Royal London Cup before England head to Spain in mid-May for a pre-Champions Trophy training camp.
Handscomb, the 25-year-old Australian batsman, is due to arrive in England three days before the Championship opener, with Yorkshire awaiting confirmation from Cricket Australia as to whether he, too, will be part of the Champions Trophy tournament that starts on June 1.
Yorkshire will have England pace bowler Liam Plunkett available from the start of the campaign, although his county and international colleague David Willey is recovering after a shoulder operation.
Willey, whose injury ruled him out of the recent West Indies tour, is set to return to first team contention for the Championship match at Southampton, when Yorkshire could be in the rare position of having their full squad available.
As ever, the issue of player availability is complex as England strive to manage workloads around the international schedule.
But Yorkshire’s director of cricket Martyn Moxon is relaxed about the situation, which affects the Headingley club more than most.
“We are where we are with it,” he said.
“It’s a situation we’re used to and one we manage as best we can.
“In Jonny’s case, he hasn’t had a lot of match-time since Christmas, but ultimately he’s not our player now.
“He’s England centrally contracted and it’s out of our hands.”
Although without Root, Bairstow, Rashid and Willey for their opening game, Yorkshire are boosted by Handscomb’s arrival.
The former Gloucestershire man has had a fine winter internationally and also gives Yorkshire another wicketkeeping option.
“We’re looking forward to welcoming Peter to the club,” said Moxon. “He’s done very well lately and is a great signing.
“Australia haven’t picked their Champions Trophy squad yet, so we don’t know for certain if he’s leaving us or when.
“I think there’s a good chance he might (get picked), but we can’t be 100 per cent sure,” Moxon added.
Of Willey’s progress, Moxon said the signs are encouraging.
“The shoulder operation was successful, and the game that we’re looking at from a first team perspective that he might be available for is Hampshire away,” he clarified.
“He’s making good progress with his recovery, and hopefully he’ll have no setbacks and be fully fit by then.”
Another pace bowler on the way back from injury is 19-year-old Matthew Fisher, who recently sustained a torn adductor.
Fisher had previously been plagued by hamstring trouble, but Moxon is confident he will be available from the start of the season.
“He’s good at the moment and will be able to bowl in matches on our pre-season tour this month,” he said.
“He should be fully fit by the time we return home, and one of our targets this year is to get our younger players really pushing the established first team players for their places, and obviously Fish is very much someone who fits into that category. He had a few injuries last year, and they’ve done all kinds of tests on his hamstring and there’s nothing alarming that shows up.
“It’s been a frustrating nine-to-12 months for him, but, hopefully, he can get through this summer without any problems,” Moxon added.
Yorkshire’s pre-season tour starts today when six bowlers fly out in advance of the main squad on Sunday.
Jack Brooks, Steve Patterson, Ben Coad, Josh Shaw, Ryan Sidebottom and James Wainman will undergo extra training to help them hit the ground running on the two-week trip.
Tim Bresnan and Jack Leaning will join the squad once the North versus South competition finishes on Tuesday.
Leaning hit 24 and Bresnan 21 in the North’s 71-run win over Worcestershire in a warm-up game yesterday in Dubai, Ben Duckett scoring 137 for the North.
Alex Lees will start the Yorkshire tour before going off to play in the Champion County game for MCC against Middlesex in Abu Dhabi (March 26-29) before returning to the pre-season trip that finishes the following day.