Are you asking how to actually implement bot AI? That's a complex field and there are lots of potential solutions.
If you're asking which side to implement it on, that'd be server side. (Though, based on your wording, it sounds like you already realized this.)
I have not done any work with AI myself. But for something pretty crude, you'll probably want to implement path-finding. If your levels aren't complicated then this can be fairly easy to do. (If they are complicated then there's also a lot of research here that can be looked over.) I think
DarkAI takes care of this, but I'm not a user so I don't know. After that, you'll have bots that probably want to kill their targeted player (maybe even each-other!). You'd just continuously update that bot's path to the player using path-finding. (Mentioned above.)
Something cool you could do is make it so that if a particular player is targeted because the bot is "mad" at him (or her) that the bot will mostly ignore other players until it finds the player. I envision a scene where the bot is walking towards you all terminator styled and some guy pokes his head out around a corner and the bot aims its gun at the head and shoots. Never taking its eyes off of you. Would be really cool and should be relatively simple (in the scope of AI implementation).
Cheers,
Aaron