Seems my assumption of “to bleed” being a positive thing (i.e.: words flow out of you like blood) is an very silly mistake in some respects. The true meaning is basically along the lines of one straining themselves to get the words out. As explained in detail on Quote Investigator, Walter Winchell attributes this turn of phrase to colleague Walter Wellesley “Red” Smith; bold emphasis is mine:
Red Smith was asked if turning out a daily column wasn’t quite a
chore. …”Why, no,” dead-panned Red. “You simply sit down at the
typewriter, open your veins, and bleed.”
Then there is some slight evidence of a positive meaning from Paul Gallico’s “Confessions of a Story Writer”; again the bold emphasis is mine:
It is only when you open your veins and bleed onto the page a little that you establish contact with your reader. If you do not believe
in the characters or the story you are doing at that moment with all
your mind, strength, and will, if you don’t feel joy and excitement
while writing it, then you’re wasting good white paper, even if it
sells, because there are other ways in which a writer can bring in the
rent money besides writing bad or phony stories.
Another turn of phrase that equated to bleeding was “drop by drop” which was used in an 1855 Harper’s Magazine article on poet Thomas Campbell; yup the bold emphasis is mine:
Campbell wrote with great toil; poetry came from him drop by drop.
Sydney Smith used to say that when he was delivered of a couplet, he
took to his bed, had straw laid down, the knocker tied up, and
expected his friends to call and make inquiries; the answer at the
door being invariably, “Mr. Campbell and his little couplet are doing
as well as can be expected!” When he produced an Alexandrine, he kept
his bed a day longer.
So knowing that, it still seems that the idea of “bleeding on the page” can be seen as a positive thing since—to some—unless you put some of yourself into your work and “shed some blood” the work itself is fairly weak, tepid. That said, generally I believe the positive modern connotation would be the words “flow through you” instead of being “bled” out.