This looks like "Quid Pro Quo" by Ray Bradbury.
He does meet this wasted talent guy while signing a book:
Santa Barbara. A small bookshop, and my signing a small novel for an even smaller group when the explosion occurred. Which hardly describes the force with which it slammed me back on my inner wall.
It began when I glanced up and saw this old, old man swaying in the doorway, dreading to enter. He was incredibly wrinkled. His eyes were broken crystal. Saliva brimmed his trembling lips. He shook as if lightning struck him when he gaped his mouth and gasped.
and rails that he should have been great:
“Shut up! God, you stupid nerveless monster, what have you done to that fine young man?”
“What fine young man?” the old, old one babbled.
“You. You. You were the genius. You had the world by the tail. You wrote upside down backwards and it all came right! The world was your oyster. You made pearls. Christ, do you know what you’ve done?”
“Yes! Nothing! And all you had to do was whistle, blink, and it was yours!”
Drags him into a time machine:
Swiftly, I hit the tabs: year/month/day/hour/ minute; and just as swiftly: state/town/street/block/ number; and yanked the backward/turn/backward bar.
And we were off, dials spinning, unspinning suns, moons, and years until the Machine melted to silence.
And shows him his younger self, who (and perhaps mixed up in your memory) kills the older version of himself (which only creates the usual time travel paradox, and then only if the younger man doesn't forget all of it and lead exactly the same life):
“Who are you really?” he said at last.
The old, old man’s voice broke.
“Son of a bitch!” cried the young man. “Damn you!”
And struck a blow to the older man’s face, and then another and another and the old, old man stood in the rain, the downpour of blows, eyes shut, drinking the violence, until he fell on the pavement with his young self astride him staring at the body.
“Is he dead?” he wondered.
“You killed him.”
“I had to.”
The young man looked at me. “Am I dead, too?”
It was collected in "One More For The Road", which, at least in one printing, was a blue book and something arguably clever was done with his name on that cover: