Strachan is able to call upon Fletcher and Bardsley for the first time ahead of the March 5 friendly against Poland while Dundee United left-back Andrew Robertson was the one newcomer in the squad.
Captain Fletcher will step up his comeback from long-term illness while the end of Sunderland full-back Bardsley's club exile has sparked an international return.
While there are three players in Strachan's 24-man squad for the first time, several regulars have dropped out and others tipped for inclusion will have to bide their time.
Rangers left-back Lee Wallace, Derby midfielder Craig Bryson, Wigan midfielder James McArthur and Blackburn striker Jordan Rhodes miss out while QPR winger Matt Phillips drops out through injury.
Strachan, who celebrated his first anniversary in the post last month, said: "This is the first time really I have had to leave out players who are doing well at their club.
"I have had to phone four, five or six and say: 'Look, you are unfortunate at this time. I think this is the squad for us. That's not to say that the next squad you'll not be in.'
"Normally it's quite easy but it's been a hard pick this time.
"There are players unfortunate not to be in the squad but we see no reason to bring them along when they are not going to play, when these guys here have definitely got a chance of playing.
"The guys who are not here, I have spoken to them in the last couple of months, and they know it's been appreciated what they have done."
Strachan only has three potential centre-forwards in his squad - Ross McCormack, Steven Naismith and Steven Fletcher, who is expected to return from an Achilles problem for Sunderland before the trip to Warsaw.
In-form strikers such as Kris Boyd and Stevie May miss out along with new Celtic signing Leigh Griffiths.
"I'm only picking a squad that will all play in a system that suits the group," Strachan said. "We are now narrowing it down to maybe two systems we are going to play. We think that's all we really need, in terms of target men, is probably three."
While Strachan found his squad in general difficult to choose, the selection of Manchester United midfielder Fletcher was far easier.
The 30-year-old, whose 61st and most recent international appearance was in a 2-1 friendly win in Luxembourg in November 2012, has now played nine times for United since returning from ulcerative colitis, the chronic bowel illness that kept him out of action for virtually the whole of last year.
"It was wonderful over the Christmas period to see him back playing football and what a Christmas present that was for him," Strachan said. "Now we are going to take it a stage further.
"I've seen him playing and he has lost none of his enthusiasm, which he will never lose to be honest. To have someone of his standing back in the squad is terrific.
"When you have medical problems, doctors do a real lot to help you out but there is also the patient themself. How strong are they? And he is strong-minded.
"I have been in contact with him now for a year. Not too much, just enquiring about his health and whether there was anything we could help him with. He has joined us in a couple of squads but for him I would imagine this will be like joining with the squad for the first time."
Fletcher's former Old Trafford team-mate, Bardsley, has seen his Sunderland career rejuvenated under Gus Poyet after he was sidelined by Paolo Di Canio.
The 28-year-old last played for Scotland during a 5-1 defeat by the United States in May 2012.
Strachan said: "Bardsley's back in there and has been a terrific player for Sunderland in the last few months.
"At this stage last season we never saw him. Now we've seen him and the more games he gets, the better he has become.
"He has been a big figure in Sunderland's improvement over the last few months."
Bardsley could be competing for the left-back slot with 19-year-old Robertson, who has impressed Strachan following his summer move from Queen's Park, notably during a joint training session with Scotland Under-21s.
The former Celtic boss said: "I saw him in the first game of the season against Partick Thistle and I thought 'you've got something. You are a bit raw... need to learn one or two things'. So we have kept an eye on him.
"He also joined us in training a couple of months back and we like him. He deserves it. He got his move to Dundee United and has been consistent for seven months."