The experienced centre-back was part of the Glovers squad that clinched promotion to the Championship last season before heading to Gigg Lane after his deal at Huish Park expired.
And after impressing during the Shakers' pre-season fixtures he has penned a deal with the League Two outfit.
Hinds was part of the Bury team who ran out 15-0 winners against St Blazey on Tuesday night in the first match of their Cornish tour.
Trialist Anton Forrester netted seven times while Tom Soares netted four in a landslide victory.
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