Like he said …
It's usually some
six-fingered bustard
that couldn't hit
a cow in the tit
with a tin cup
that does you in.

This message has been deleted.

The Metropole (the Constantinope, or "Connie" in the novel) did, however, award him Employee of the Year, posthumously.

I would say it was a combination of wanting to make a name for himself by being the one to take out Books, and his contempt for Books for shooting up his place and killing his faro dealer.
It doesn't seem likely to me the bartender knew ahead of time what was going on. Because when Pulford comes in asks him why he is there so early and Pulford tells him he is expecting someone.
My guess is he probably planned to tell everyone he shot Books in self defense after Books gunned the other three down thinking he'd be hailed as some kind of hero. He obviously did not count on Gillom showing up.

The bartender knew what was happeningSo did everyone in town. That is why The Doctor, Bond and the other were outside.
The bartender saw Books off Sweeney, Bulford and Cobb.
Strangely, Books was shot in the armsIt may not have been a mortal wound.
The bartender was a coward and an opportunist who shot Books in the back.

YOUR COMMENT JUST GAVE AWAY THE ENDING OF THE MOVIE !!! YOU SHOULD EDIT THE TITLE TO SAY
"Spoiler Alert Question about the bartenders actions"
Geeeeze

That, perhaps. On the other hand, Books was a notorious gunman who had just killed three people in his bar, including the establishment's own faro dealer. The bartender had been in the back room during the shooting; so, theoretically, it's conceivable that he thought that Books had murdered them and, possibly, might have gone on to murder others - including, had Books turned on his way out, perhaps the bartender, himself. The viewer knows better, of course, but that could, theoretically, have been the bartender's thinking.