Root (133no) was required in only the third over of England’s Group A chase of 305 for six after Jason Roy’s poor run of form continued with just a single on his home ground.
Alex Hales (95) was the dominant presence in a second-wicket stand of 159 which put England on course to outdo Tamim Iqbal (128) and Mushfiqur Rahim (79).
Root and Eoin Morgan (75no) did the rest in another unbroken three-figure partnership as the hosts got up and running with eight wickets and 16 balls to spare.
Root was noticeably inconvenienced by a sore right leg, although it is Chris Woakes’ side strain which is likely to be most significant for England.
Liam Plunkett (four for 59) was England’s banker with the ball after Woakes left the field having bowled only two overs, but a longer-term replacement may be required over the next two-and-a-half weeks.
Tamim put on 166 runs for the third wicket with Mushfiqur, passing his ninth one-day international hundred from 111 balls as he paced an assault which brought Bangladesh 83 in the last 10 overs - despite the dismissal of both set batsmen to successive Plunkett deliveries.
When England batted, but Roy was left to reflect on his fifth single-figure score in his last six ODI innings after paddling an attempted ramp-sweep just within the clutches of short fine-leg – where Mustafizur Rahman held a memorable leaping catch.
Hales and Root responded with a calm authority, picking off the boundaries but taking few undue risks until – with the opener’s hundred only one more big shot away immediately after hitting Sabbir Rahman for his second six to add to his 11 fours, he found the hands of deep midwicket in the part-time leg-spinner’s solitary over.
Root had already hurt himself setting off for a run. But after Morgan escaped a close call on 21, Tamim far from amused to see his tumbling take ruled no catch at long-on because the ball was grounded, England’s No 3 dug in to pass his 10th ODI century with a trademark scamper for two into the leg-side to add to his tally of 11 fours and a six.
Woakes had begun the tournament with a maiden, after England chose to give the tourists first use of a very good pitch on a glorious morning, but he was out of the equation all too quickly.
Moeen Ali put down a straightforward chance in the same position, reprieving Soumya Sarkar - who was unable to take significant advantage before cutting a slow long-hop in Ben Stokes’ first over straight to Bairstow in the deep to end an opening stand of 56.
New man Imrul Kayes edged Stokes through a vacant slip to get off the mark, but that was not especially costly either as the No 3 was soon very well-caught by a diving Mark Wood at mid-on off Plunkett.
Stokes made up most of the shortfall as it became clear Woakes would not bowl again.