Bell, whose second innings 109 set up Ashes-holders England's tense 14-run first Test win over Australia in Nottingham last week, was 62 not out after adding 99 for the fourth wicket with Warwickshire colleague Jonathan Trott (58).
Jonny Bairstow, 'bowled' by Peter Siddle on 21 only to be reprieved by the third umpire checking for a no-ball, was 28 not out having helped Bell compile a fifth-wicket stand so far worth 56 runs.
Trott, often criticised for slow scoring, struck 11 fours in almost giddy fashion before he became recalled Australia quick Ryan Harris's third wicket of the innings.
After the teams were presented before play to Queen Elizabeth II, monarch of both Britain and Australia, it was the tourists who bossed the early exchanges.
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England were soon three wickets down with Cook, opening partner Joe Root and dangerman Kevin Pietersen all out cheaply.
Harris, recalled after Australia dropped the wayward Mitchell Starc, then took two wickets in an over.
The 33-year-old, playing just the 13th Test of his injury-ravaged career and first in more than a year, then struck with the second ball of his third over when he had Root lbw for six.