Bans in ARAM

You've been looking at it from the wrong angle, don't add bans to stop other players from playing something you dislike to play against. Add 1 ban which acts as a personal ban of a champion which you won't be able to roll in that ARAM match, it is not much but if you are thinking how to implement bans and keep the casual/enjoyment level of people who just came to chill for a bit this can help, since everyone has something they aren't good at, you can look at it as a free reroll each match.