Bell opened the batting for England and made 58 before he was stumped by Shaikh off the bowling of Yeligatti.
Shah hit 83 before Andrew Flintoff came in to fire a century off 85 balls and put England on 297-4 after their allotted fifty overs.
In reply, Sheyte made fifty for Mumbai but James Anderson took three wickets to restrict the home side to 175-8 and give England a win by 122 runs.
Warwickshire boss Ashley Giles was in charge of the England side which won the Hong Kong Cricket Sixes. They beat Australia with the last ball of the final by virtue of fewer wickets.