Narin Guran's uncle was arrested last week on suspicion of murder
For long periods it wasn't sparkling, but it was effective, and after Finch was out for 53, Warner kicked on to score a hugely impressive 166.
That took his tournament-leading aggregate to 447, with Finch running third on 396. Only against West Indies have they failed to get their team off to a great start - five times making at least a 50-run partnership.
It meant Usman Khawaja was allowed to play at his pedestrian pace for 89 without pressure. On a high-scoring Trent Bridge pitch, that might have been more of a hindrance than a help, but a late blast, headed by Glenn Maxwell's 32 in 10 balls, took them to a tally that proved 48 too many for Bangladesh.
"We've been pretty consistent, it's just nice to get the side off to a decent start," Finch told reporters after Australia's fifth win in six games put the defending champions top of the standings and firmly on course for the semi-finals.
"The wickets have been nice to bat on, not much movement, ball pretty low, so its a good combination for an opening batsman," Finch added.
Warner is certainly experienced, though he has looked a different type of player since his return from being banned for his part in last year's ball-tampering scandal.
Previously a powerful, brash hitter who showed utter disdain for his rivals, he is now more circumspect.
CUTTING LOOSE
His two slowest career ODI 50s have come in this tournament and he was going along a well under a run a ball on Thursday before cutting loose to finish with 14 fours and four sixes.
"It's not like we go on purpose and not try to score but you have to respect the new ball and the bowlers bowled well," Warner said.
"It gets a bit frustrating because you sort of middle one and it goes full pace to the fielder. That's been a bit annoying but I've just hung in there.
"I got frustrated against India. I got frustrated against Afghanistan. And then today, Finchy kept telling me to hang in there and bat deep and bat time. It must be a bit more maturity, I think."
Veteran Australian commentator Jim Maxwell said he thought there was a twin explanation for Warner's change in approach.
"Partially his elbow (injury) and partially what happened to him," he told BBC Radio. "He is a chastened individual coming out of a pretty grim period - a lot of people thought he should never play for Australia again."
Warner said his time away from the game had helped freshen him mentally and physically.
"It means a lot to us, but it means a lot to our country," he said. "That was obviously a dark year for Australian cricket so we've just got to keep winning for our country, doing the best we can, putting our best foot forward."
Narin Guran's uncle was arrested last week on suspicion of murder
US central bank focused on cooling labour market
More than 100,000 left-wing demonstrators rallied across France on Saturday to protest against Barnier's nomination as PM and denounce Macron's 'power grab'
The outdoor destination is home to over 3,000 animals representing 78 mammal species, 50 varieties of reptiles, and 111 kinds of birds
Since the case was brought, Google has rebranded its Bard AI product to Gemini
Data revives fears that months of elevated borrowing costs have already started to pressure the economy
This comes two weeks after a massive police manhunt for the politically connected preacher
Debonair by Andrea Blk is preparing to relaunch with a new collection