This is an example of a wanted poster from 1864 and another one from 1881. Here is one for Bonnie and Clyde that is very similar to wanted posters of popular media. While not all posters were similar to the ones portrayed in the old westerns of Hollywood, these portrayals do have a root in actual history.
I made an answer to a similar question a while back that might prove interesting to you.
It's worth noting that the reward for Billie the Kid was to be paid on his "capture and delivery," while Pat Garrett collected it for killing him. Edit: I made a mistake. Garrett collected it for capturing him alive. I'll leave the note, with the strike-through, because it led to some questions. :)
Here's one case in which a dead-or-alive bounty was collected. The Dunn brothers killed two wanted men and brought them in for the reward:
May 2, 1895, Dunn Ranch on the Cimarron River, Oklahoma. Charley Pierce and Bitter Creek Newcomb approached the Dunn Ranch after dark and went into the barn to stable their horses. The two men were wanted by the law, and there was a five-thousand-dollar dead-or-alive reward out for Newcomb. Bill [Dunn] and a brother picked up shotguns, and when the outlaws emerged from the barn, they were shot down in front of the house. Pierce groaned and was shot again. The next day the outlaws were taken into Guthrie for the rewards.
Taken from the Encyclopedia of Western Gunfighters.
The four thousand dollar bounty for John Wesley Hardin was also dead-or-alive. It's what Texas Ranger John Riley Duncan, who was involved in the capture of 21 fugitives for the reward, was pursuing when he aided in the capture of Hardin. Hardin was taken alive.
