The conflict of "The Bride Comes to Yellow Sky" is best identified as Human versus Self. The Marshall goes to San Antonio to see a woman he has either met on an earlier trip or has heard of:
[he] had gone to San Antonio to meet a girl he believed he loved,
Potter, the Marshall, knows that society does not allow for secret marriages, especially when there are many friends to be consulted and confided in and, even more importantly, public officials to consult and confide in; secret marriages were looked on with serious disfavor:
[he] induced her to marry him, without consulting Yellow Sky for any part of the transaction.
The Marshall knows that Yellow Sky looks up to him and depends upon him, thus his actions weigh heavily toward their happiness. As the town friend and protector, he feels his duty toward them in a particularly serious vein:
people in Yellow Sky married as it pleased them ...; but such was Potter's thought of his duty to his friends, or of their idea of his duty, ... [that] he felt he was heinous. [...]
A sense of mutual guilt invaded their minds and developed a finer tenderness. They looked at each other with eyes softly aglow. ... The traitor to the feelings of Yellow Sky narrowly watched the speeding landscape.
Though the Marshall knows all these things about Yellow Sky, he cannot bring himself to stop and act in accord with what he knows in his conflict with himself:
Frequently he had reflected on the advisability of telling them by telegraph, but a new cowardice had been upon him.
This conflict extends symbolically to his ability to perform his duty as Marshall. When we meet Wilson, we are told by the townspeople's conversation how much they trust and rely upon the Marshall to keep them safe through his unquestionable courage and integrity. The implied extension of the Human versus Self conflict is the question of whether the Marshall will wane in courage now that he has a bride to protect. This is the significance of the conflict with Wilson. While Potter's bride is standing at his side, without a gun on his person, the Marshall stands up to Wilson's drunken rage without a quiver or a hesitation.
Now his conflict against himself is wholly resolved: (1) he knows the town will accept his secret marriage because he and his bride have both survived the crucible of fire (Wilson's gun-waving challenge) and (2) Potter has confirmed for himself and the town that his courage and integrity have not and will not wane as he is unflinching in courageously performing his duty.
"[If] I'd thought there was going to be any galoots like you prowling around when I brought my wife home, I'd had a gun, and don't you forget it."