Former captain Sunil Gavaskar was the only Indian included in the controversial team which has Pakistani all-rounder Imran Khan as the captain.
Besides the omission of Tendulkar and Bradman, Bird's team did not have the greats like Brian Lara, Ricky Ponting as well as the West Indian fast bowlers Malcolm Marshall, Andy Roberts, Joel Garner and Michael Holding.
Others in the team, named by Bird in an interview with London newspaper 'The Telegraph' ahead of his 80th birthday today, are Barry Richards, Vivian Richards, Greg Chappell, Graeme Pollock, Gary Sobers, Alan Knott, Shane Warne, Dennis Lillee and Lance Gibbs.
Former India captain Ajit Wadekar felt Gavaskar was the right choice in the opener's slot but said that he was surprised by the exclusion of Tendulkar, Bradman and the West Indian fast bowlers.
"It's a bit partial. He has selected only players whom he has seen from close quarters. But the combination is not balanced. Of course, Gavaskar will have to be there. But it is surprising that there is no Sachin Tendulkar, Don Bradman and the West Indian fast bowlers," he said.
"And who will be the new-ball partner of Lilee? It's also surprising there is nobody from among the famed Indian spin quartet of Bishan Bedi, Erapalli Prasanna, B S Chandrasekhar and R Venkataraghavan. It would also been ideal if Adam Gilchrist was there in place of Allan Knott," he added.
Former India batsman Chandu Borde said leaving out Tendulkar and Bradman from his team showed Bird's lack of cricketing knowledge.
"That's his opinion. He must not have seen Bradman playing." he said with a sarcastic tone.
"By this team, one can see how good is his cricketing knowledge. Statistics will tell you about Bradman and Tendulkar. One need not refer to his eleven. From my point of view, it's the English media which has made Bird an umpiring legend. He's always bias."
Former India captain Nari Contractor wondered on what basis Bird chose his team which did not accommodate the likes of Tendulkar and Bradman in it.
"These are individual opinions. But I don't know on what basis he has chosen the team. We all know about Bradman and Tendulkar. Like them, many others like the West Indian quartet (Michael Holding, Colin Croft, Joel Garner and Andy Roberts) are also not included," he said.
Contractor, however, said that the team was Bird's individual choice and and would no doubt invite arguments.
"He might have not chosen Tendulkar as he would have thought that the Indian batsman had not faced the best fast bowling attack. It's his reasoning having seen the players from the middle. I don't know why are you doubting Bradman and Tendulkar. This maybe food for some and poison for others. He has chosen his countryman Alan Knott as the best wicketkeeper batsman. For the sake of it, one can keep on arguing. But that's his opinion and it's the end of matter," he said.
Another former India player Shivlal Yadav could not believe Tendulkar and Bradman were not there in the all time Test XI.
"I'm definitely surprised that these two names -- Bradman and Tendulkar -- don't figure in his list. By their sheer performance they have shown the world what they are capable of. They have outclassed everybody else and have rewritten the record books. There is no doubt that the duo should have been part of the Test XI," he said.
"But this is his opinion. Everybody has got the freedom to express his or her opinion. Dickie Bird is a legendary umpire. I cannot say it's wrong. But I don't know on basis of what parameters he has chosen the team."
Former India all-rounder Bapu Nadkarni said, "It is his personal opinion and not much fuss should be made out of it. I am surprised Malcom Marshall was not there. Bird was a respected umpire. But team selection is different from umpiring."
Prasanna also said that it was upto Bird to pick his World XI team.
"That's his pick. I can't comment on somebody's personal assessment. Having seen the players from the best possible view -- by being on the field -- he has made his Test XI. I would have been rather surprised had there been a voting and these players like Tendulkar and Bradman were omitted on basis of that," he said.
Former captains Dilip Vengsarkar and Krishnamachari Srikkanth refused to comment.
"I don't wish to comment on this," said Vengsarkar.