The visitors raced into an early lead after Olivier Azam stole a Bristol line-out and Peter Buxton powered over.
Jason Strange kicked two penalties for Bristol before Simpson-Daniel twisted his body to touch down after chasing Ludovic Mercier's grubber-kick through.
Mark Cornwell picked up a loose ball to add a third try while Simpson-Daniel crashed over to earn a bonus point.
Bristol coach Richard Hill:
"I think we were lucky to be in the game. The scoreline was reasonably close for a while but we didn't deserve it to be that close.
"The same old things were cropping up. Turnover ball and the penalty count against us was again high. We don't seem to be learning so we need to work some things out.
"We were pretty poor while Gloucester are a side who are continuing to get better and their forwards were just too strong for us."
Bristol: Stortoni, Marsden, Higgitt, Contepomi, Lemi, Strange, Rauluni, Hilton, Nelson, Crompton, Sambucetti, Llewellyn, Salter, Ward-Smith, Lewis.
Replacements: N. Clarke, Winters, El Abd, Going, Gray, Denney.
Gloucester: Thirlby, Garvey, Fanolua, Allen, Simpson-Daniel, Mercier, Thomas, Collazo, Azam, Vickery, Eustace, Cornwell, Buxton, Boer, Narraway.
Replacements: M. Davies, Wood, Brown, Hazell, Richards, B. Davies, Paul. .
MMIX
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