Here's my attempted transcription of the lyrics as sung by the Bogtrotters (Fields Ward, Crockett Ward, Eck Dunford) in their 1937 Library of Congress recording. Notably, Crockett learned his rendition of the song in 1896 in Smyth County Virginia by a man he identified as Freeling James, who had moved to Virginia after living in Missouri during 'the raids' in that area.

Notably, the recording is similar (but not the same as) a recording from the Bogtrotters released on Folkways Bluegrass From the Blue Ridge: Country Band Music of Virginia. Unfortunately, the verses I'm least sure about were, naturally, not repeated in that rendition. I have marked that section with brackets ([[ and ]]).

Transcription by ear from The Bogtrotters: 1937-1942, Biograph RC 6003

JESSE JAMES

Jesse James was a man who had traveled through the land
And he traveled on both night and day
He was shot on the fly by little Robert Ford
And they laid Jesse James in his grave

Jesse James went to town not many days ago
And the bank was opened for the thief
The clerk got down upon his knees and he handed up the keys
To Frank and his brother Jesse James

Jesse James, Jesse James, there's no more of Jesse James
Robbing the banks and trains
He was shot on the fly in the twinkle of an eye
And the legend of James never dies

Jesse James had a wife, she lived a mourner all her life
And the children were running 'round brave
She mourned his loss [[as a loot giver too]]
As a guerrilla in Missourah he was brave

The boys in the West, when they heard of Jesse's death
They wondered what caused him to die
Was a cold pistol ball, brought him tumbling from the wall
And they laid Jesse James in his grave

Jesse James, Jesse James, there's no more of Jesse James
Robbing the banks and trains
He was shot on the fly by little Robert Ford
And they laid Jesse James in his grave

Frank James thought it best when he'd heard of Jesse's death
To abide by the laws of the state
He applied to Governor Crittenden* in a long written letter
And explained the course he's going on to take

Frank James is at ease in the state of Texas
And at Denver he resides
It's been many men called their presence for to be
For the name has reached across the sea

Jesse James, Jesse James, there's no more of Jesse James
On the Richmond and Danville Trains
He was shot on the fly by a little Robert Ford
And they laid Jesse James in his grave

* Pronounced more like "Gritten" but Crittendon is close enough and was indeed the governor of Missouri in 1882, the year of James' death.