The Meaning of Bleeding/Stop the Bleeding in Golf
The "bleeding" in those phrases refers to bleeding strokes: the golfer who is playing poorly is bleeding strokes, meaning losing strokes to par. If Golfer X started "bleeding strokes on the third hole," that golfer might have made a double bogey on the third hole, then followed it up with a couple more bogeys. The specific scores change, but the meaning stays the same: a golfer who is "bleeding" is dropping shots to par through poor play and miscues.
And "stopping the bleeding"? Of course, that means getting your poor play under control again. A golfer who "needs to stop the bleeding" is one who is not playing well and needs a good, solid stroke or one good hole to right the ship and get the round back on track. Saying, "I stopped the bleeding with a par on the sixth hole" implies that the holes before No. 6 didn't go so well for the golfer.
As an example from the world of major championship golf, consider what the New York Post wrote about Tiger Woods' second-round play in the 2022 Masters Tournament.
"Woods got off to a rough start in the second round, bogeying four of his first five holes. That dropped him from a tie for 10th at the start of the day to a tie for 39th," the Post's reporter wrote. But, the writer said, Woods "... finally stopped the bleeding with a two-putt par on the par-3 sixth."
More golf lingo: