Warne, revisiting a theme he favoured during Australia's 3-0 Ashes defeat in England last summer, has suggested the tourists may well be about to lose the urn unless Cook changes his ways.
The former Australia leg-spinner branded Cook's captaincy as "negative, boring" as the side prepare for their second tour warm-up game against Australia A ahead of the first Test in Brisbane which starts on November 21.
Bell is an old hand at deflecting Warne's jibes, from the latter's playing days right through to his current habitat in the commentary box.
He shrugged his shoulders at the former spinner's remarks, which not for the first time included a dig at Cook's tactics.
"It's quite funny at times," Bell said.
"I've certainly learnt over time that there's no point wasting energy trying to find compliments from Australians.
"It's just not going to happen.
"We could win 5-0 and still have negatives from Australia, so I'm not going to waste any energy any more worrying about it - and I don't think the other lads will either.
"That's how we feel.
"At the end of the day, we've just got to go out and do what we do and look after the team and the environment we have and go out and win."
Warne had blasted Cook ahead of this winter's Ashes series and questioned his style of captaincy.
The 44-year-old laid into the Cook during the Durham Test, just before Stuart Broad kick-started a collapse which gave England outright series victory for a third successive time.
Warne told national newspapers: "He can be negative, boring, not very imaginative - and still win and be happy.
"But I'll tell you my opinion - I think Alastair Cook has to be more imaginative.
"I think if Australia play well, and he continues to captain the way he does, England will lose the series.
"He lets the game drift."
Joe Root also has no intention of listening to Warne's opinions about his batting technique, but can assure him he will be no sacrificial lamb to the slaughter in Australia.
Twenty-two-year-old Root has had less experience of the great leg-spinner's verbal jousting, the latest instalment of which is that the young Yorkshireman needs a break from opening the batting if he is to avoid being "crucified" by Australia's bowlers on bouncy pitches in the forthcoming Ashes series.
"I don't know why he said that," Root said.
"I think typically, when they toured England, they had a very distinct way of attacking us in the media - and that's one way they go about things. Well, (it's one way) he goes about things.
"But that's not for me to worry about.
"I can only prepare for what I'm going to be doing, and it would be wrong for me to look at things like that.
"I can only concentrate on my cricket."
Root, whose close encounter with Australia opener David Warner's fist in a Birmingham bar was such a controversial preface to last summer's Ashes, knows there will be 'banter' this winter from crowds, media and players alike.
"I obviously expect them to talk about hard cricket and how hard it's going to be over here, and how good they are," he said.
"But that's Australia. You wouldn't expect anything else.
"I don't think Shane Warne's ever said a nice word about an England touring team, so I think it would be wrong for me to listen to everything he says.
"But I'll definitely be making sure I prepare well going into that first Test match."
Root had scarcely set foot inside the Bellerive Oval, venue for England's second tour match against Australia A this week, before he was answering a provocative question about his own surname.
'Do you know what it means in Australian?' came the inquiry from a radio interviewer.
The answer, apparently, is an irreverent term for having sex.
Root was not fazed, and said later: "That's been mentioned a few times.
"I could get a bit of stick about that in the next few months, and I'm quite looking forward to seeing what they come up with.
"It will be quite interesting."