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.
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.
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.
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