I am on the mobile version and I am looking for a beehive, but I can't find one.
Since bee hives are biomes, they are actually spawned at world gen. First, your world must be generated in 1.2 and above for it to have any chance of been generated with the bee hive mini-biome. Your game need to have a minimum version of 1.2.6508 on iOS and 1.2.6667 on Android when the world was generated.
The wiki also states that in 1.2.4 the spawn rate was increased, but the the 1.2 update for mobile only brings them up to the equivalent of 126.96.36.199 on the PC. Other than that, information on the actual spawn rate is sparse.
Anecdotally, your world will almost certainly have at least one or two of these in the underground jungle. The challenge is actually finding them, since the underground jungle rates as one of the most dangerous biomes both pre- and post-hardmode.