its possible to play with bots offline, including using custom bots, also its possible to play in lan using the developer console (no user interface as the lobby system need internet) but the bot works in the game interface.
Topic on Talk:Dota 2
No. This game has have Online Only DRM, you cannot play with bots in offline.
@Posedennetshow I didn't test playing in LAN, but it is possible to play vs bots in offline mode (though it's solo only, and you can't even choose modes like turbo). Demo hero too works offline.