How do you get the Season 2014 - 3v3 Bronze?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Bronze in the 2014 ranked season in 3v3.”
Is the Season 2014 - 3v3 Bronze still available?
No. The Season 2014 - 3v3 Bronze was a ranked reward: to get it you had to reach Bronze in Twisted Treeline 3v3 during Season 4 (2014). Riot does not give out past ranked rewards again, so it cannot be earned anymore.
