England, who at 3-0 up had already won the five-match series, were 247 for four at stumps, still 245 runs behind Australia's first innings 492 for nine declared but needing just 46 more runs to avoid the follow-on.
Bell, who came into this match having scored exactly 500 runs in the series with three hundreds, was 29 not out off 110 balls in nearly two-and-a-half hours at the crease.
Meanwhile Test debutant Chris Woakes, Bell's Warwickshire team-mate, was 15 not out following a final session played under gloomy skies despite the glare of the floodlights. See in Pics
Several England batsmen got in but failed to press on, with Kevin Pietersen making an unusually restrained 50 in 133 balls.
England scored 215 runs in the day's 98.3 overs, the run-rate rarely rising above two an over, in a match where victory would mean they had won four Tests in a home Ashes for the first time.
But there was still something to be gained for England by denying their arch-rivals a consolation success -- Australia's last 'winless' Ashes was in 1977 -- ahead of the return series 'Down Under' starting in November.
England resumed Friday on 32 without loss after Shane Watson's Test-best 176 and Steven Smith's 138 not out -- his maiden hundred at this level -- had taken Australia to their imposing total.
Alastair Cook, the England captain, was 17 not out and Joe Root 13 not out.
The openers made a solid start, with Root clipping Ryan Harris off his legs for four while left-hander Cook square-drove the fast bowler for a boundary.
But Cook's poor series with the bat continued when he followed a delivery angled across him from Harris and edged to wicketkeeper Brad Haddin for 25.
It was an all-too familiar exit for Cook in a series where he has scored 243 runs in nine innings with a best of 62 at an average of just 27 -- a far cry from his triumphant 2010/11 Ashes tour of Australia where he made 766 at 127.66 with three hundreds.
Root's pull off Peter Siddle saw him to a 145-ball fifty with eight fours, but, after lunch, he made a tame exit on 68 when he fell into an obvious trap by top-edging a sweep off spinner Nathan Lyon straight to Shane Watson at short fine leg, with England now 118 for two.
There were ironic cheers from a capacity crowd when Pietersen drove leg-spinner Smith for four -- the first boundary in 11 overs.
But the first delivery with the new ball saw Jonathan Trott lbw for 40 to left-arm paceman Mitchell Starc.
England challenged but, with the Decision Review System upholding Pakistani umpire Aleem Dar's verdict, it was the end of Trott's 134-ball knock.
By contrast Bell, a Warwickshire team-mate of Trott, got off the mark fifth ball with a square-driven four off Starc.
Pietersen's bottom-edged boundary -- England's first in 14 overs -- off Test debutant James Faulkner saw him to a fifty on the ground where his stunning maiden century at this level secured an Ashes-clinching draw eight years ago.
However, Pietersen had failed to add to his total when he edged Starc to Watson, now at first slip, to leave England on 217 for four.
Woakes's medium-pace posed little threat in Australia's innings but the all-rounder's batting suggested greater promise as he got off the mark first ball with a cover-driven four off Starc.