The hosts and favourites started with a convincing win over South Africa and have bounced back from a surprise defeat to Pakistan by brushing aside the potential banana skins of Bangladesh and the West Indies.
Bairstow, part of a core group who will also be eyeing Ashes glory following the conclusion of the tournament, insists there is plenty more to come from the one-day side.
He said: “To be able to hopefully say that you’ve played in both and, hopefully, won both – that’s the big thing, that’s what you want to be doing – is something that you look back on.
“Everyone talks about those moments, ‘something to tell the grandkids’, it really would be something to tell the grandkids.
“To be part of a side that’s got the potential to win the World Cup, especially at home, is spine-tingling, to be quite honest.
“There will be a lot of emotion going through everyone but at the same time we need to work hard and get there. It’s alright talking about it but if you don’t get there, then it doesn’t matter.
“Generally, I think that we’re playing pretty good cricket. There’s still a lot that we can improve on to get that perfect game.
“There’s enough games left in order to keep pulling those together and, hopefully, they come in the latter rounds of the competition.”
Bairstow was dismissed for a golden duck on his tournament bow but he has rebounded by registering 32, 51 and 45 on his last three visits to the crease, healthy contributions without being match-shaping.
Yorkshire team-mate Joe Root has already amassed two tournament centuries, with fellow opener Jason Roy and Jos Buttler also going to three figures, and Bairstow is convinced a momentous innings of his own is forthcoming.
He said: “I feel good. Obviously I want to get a couple of big scores. I’ve started off alright and I’m striking the ball well so it’s just a case of when it clicks.
“And then when you go big and you go really big, that’s all it is. But we’ve been lucky enough that we’ve had four hundreds in four games. Joe’s got two, Jos has got one and Jason’s got one, so I’m due. And it’s all the Js – I’m next!”
Bairstow, speaking at an event for Booking.com, accommodation and attractions booking partner for the World Cup, added: “We’ve got confidence in our whole line-up. You could see that with (Chris) Woakesy coming in at three the other day, he wanted to open!
“It wasn’t massive panic stations because we’re very fortunate to have people at nine, 10, 11 that can come in – Adil Rashid has got 10 first-class hundreds so to have him coming in at No 10 is pretty handy.
“We’ve played well over the last 18 months so it doesn’t just go after losing to Pakistan in one game.”
Roy has been ruled out of England’s matches against Afghanistan and Sri Lanka with a tear in his left hamstring but captain Eoin Morgan’s back injury will continue to be assessed.
The pair limped from the field during England’s comfortable victory over the West Indies in Southampton, with scans taking place over the weekend.
Roy will play no part in this week’s double-header, though the lack of a clear rehabilitation period will lead to fears that his absence could be longer.
Morgan, who suffered a painful back spasm at the Hampshire Bowl, has responded to treatment and received a more optimistic prognosis.
The captain could still feature at Old Trafford today but given his importance as a batsman and leader, it is unlikely any gamble would be taken with his long-term fitness.