I've use heat to remove many recalcitrant lables / tags / stickers. In the case of bottles, with wraparound, glossy (probably waterproof...) labels, the boiling water trick is very efficacious. I would avoid shattering (from too sudden a temperature rise) by first filling the bottles with hot water from the (~ kitchen) tap to start them up the temperature scale.
While that 'soaked in', I would boil water in an electric jug ... tip out the hot tap water ... carefully refill with boiled water - avoiding wetting the label, since that might weaken the paper and make it harder to pull it off the bottle as the adhesive softens. A small slit at the edge might be necessary to lift a clean-edged corner ... and you ought to be able to carefully peel label off - complete with most of its adhesive.
Hang onto the removed label ... once the bottle cools down, any residual adhesive may be lifted off by pressing the sticky side of the removed label over the errant adhesive. If that doesn't work, a solvent is needed ... I would start with one of the essential oils mentioned, rather than spirits - but all should work.