Most people understand golf as a game where golfers hit a stationary ball. The ball doesn't move when a golfer makes a stroke, and that's one of the most taunting parts of the sport. It's right there, staring at the golfer the whole time.
Keeping that in mind, under the Rules of Golf, it's expressly against the rules of the game for a golfer to hit a ball or putt a ball while it's still moving -- be it bouncing, rolling on the putting surface or even in the air. The ball has to be at a complete stop when a player hits it, or otherwise the golfer is breaking Rule 11-2, formerly Rule 14-5.
From the Rules of Golf, here's Rule 14-5:
A player gets the general penalty if they deliberately deflects or stops any ball in motion.
This is true whether it is the player’s own ball or a ball played by an opponent or by another player in stroke play.
A player is excepted from the rule when the ball is on the tee, is moving in a water hazard or is struck more than once.
The language of the current Rules of Golf is slightly different than the prior version, which covers this topic under Rule 14-5. There's also penalties that can come into play separate from this one if a player causes a ball to move and/or doesn't replace it to the original resting place before hitting it.
Now, there's also the consideration for a "serious breach" of the Rules of Golf, which would cover when a golfer hits a ball while it's still moving knowing that it would help them save strokes or was a violation so blatant it was unbecoming of a golfer. In that case, the player would then be disqualified.
There's also consideration under Rule 1-2, which would constitute when a player is "taking action with the intent to influence the movement of a ball in play." That would mean stopping or deflecting the ball so as to gain an advantage. The penalty for that is disqualification.
