Create a prize, and in the Recipient section select "Bounty on player:", and select "(Random Player)" in the player drop-down list.
To display the recipient when the prize is awarded you can do one of two things (or both).
1) Use the <prizes> token to display the prizes and their recipients. You'll need to read up on the Layout section in the user manual to really understand this. But if you are using the default layout, edit the "Prizes" cell and change the HTML from:
<prizes orient="horizontal">
to
<prizes orient="horizontal" showRecipients="true">
Make sure to do this on the "Even Rounds" tab, too.
2) Create an event that fires when the random player is chosen, and add an action that displays a message (and/or plays a sound). To do this, create a new Event, select "create a new event from scratch", enter a Description, and select "a random player is chosen for a prize" in the Trigger drop-down list. Add an action and select "Display message". Set the text to:
Random bounty on <randomname> won by <hitman>
or, obviously, whatever you want. "<randomname>" will be replaced with the name of the player chosen as the random bounty, <hitman> will be replaced with the name of the hitman. There are other tokens you can insert into the text - press the "Insert Token" button to see them.