Originally Posted by jolly_ross

"Use compressed air" is like the recipe for rabbit pie which starts "first you catch the rabbit ..."
This is oversimplifying a difficult thing - most people do not have a compressor. Compressed air is a shop trick.

If you're not over fussed about possible small scratches on the bars along where the new grips will go try this ...
Loosen brake/gear levers, move them inward along the bars so they're out of the road.
Adjust a pair of vice-grips (or mole-grips, or slip pliers) so that the jaw gap is just larger than the bar diameter, but still less than the grip diameter. Close jaws around the bar on the inside of the grip, then use the tool to push the grip off.

Admittedly this does assume you have a pair of vice grips or the like.