The 69-year-old Bishop said he punched Barron, 65, in the head after the senator called him a "son of a bitch."
"I responded to his comment with my right hand," Bishop said.
Barron denied saying that to Bishop. He said the Jasper senator used an expletive to him and he was trying to get away when he was hit by Bishop on the side of the head near an ear.
The Senate later considered censuring Bishop and expelling him from the chamber for the remainder of the day, but Bishop said that wasn't necessary and walked out of the Statehouse, saying he was going home to Walker County.
"I love every one of you. Most of all I love this chamber. I'm going home and you all have a good day," Bishop said in an emotional speech before his departure.
Bishop, a coal mining executive from Walker County who once challenged another senator to a fistfight, said he regretted the incident because "that's not the way grown men solve their problems," but he said he would not immediately apologize to Barron.
Bishop said he responded to Barron's comment in the way he learned as a child in Moro Bottom, Ark.
"I was raised in the woods of Arkansas and people don't say that about your mom," Bishop said.