Riot does not employ bots in modes not designed for them (vs. AI, customs, Doom Bots etc.), so if you encounter a bot where a player should be it's because the player is using an illegal program (likely to level or farm IP) and you should report it under the "Cheating" category with a description.
As for sometimes getting them in ARAM, if your MMR is low you might come across them way more than normal; they can't win much so they don't climb, and get banned before they do. If you can win enough and get your MMR up you won't see them ever again, but since bot bans are done in waves and can take a week or two after detection to be banned sometimes, lower MMR gets stuck with them occasionally.