Pokémon X and Y Walkthrough, Pokémon Move Sets: Bibarel
(Please note that the recommendations below are largely made for in-game play. A Bibarel in a competitive environment - won't see that very often - will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you have different moves in mind for a Bibarel, share them in the comments.)
There's a fairly expansive selection of misfit pokémon that few (any?) people bother to use, and Bibarel is high on the list. Its stats are bad, its move pool is a little lame, and... uh... it just looks dumb. Bibarel doesn't have much going for it. Sometimes it's fun to find the positives in life's losers, though, and you can really shame online X and Y opponents by bringing them down with a Bibarel. This article will help you craft a serviceable Bibarel. (Try not to be too shocked if it doesn't work to your expectations.)
Type: Normal / Water
Bibarel's pretty standard, as far as pokémon go. It starts off as the infamous Bidoof; level Bidoof to 15 and you'll have yourself a Bibarel.
Fire, Ice, Steel, Water. Immune to Ghost.
Electric, Fighting, Grass.
Bibarel is largely a subpar pokémon. Its top stat is Attack, which, sadly, is just a teensy bit over average. Everything else is either average or below average. Most abysmal is Bibarel's defensive capabilities, which, despite how bulky it looks, are below average. You'd probably be better off trying to raise its HP, which is at least average. I suggest working to get a suitable Nature, as well, since Bibarel can really use every advantage it can get; Adamant or Jolly are preferable.
Simple: This pokemon's stat boosts are doubled. If Bibarel was to use Amnesia, for example, its Special Defense would be raised by four stages rather than two. This is actually a relatively good ability if used in conjunction with, say, Amnesia, but Bibarel lacks some of the best moves that would make this ability really shine.
Unaware: This pokémon ignores stat changes, period. This applies to itself as well as to others, so a pokémon that used Swords Dance would find itself doing no extra damage to the Bibarel. This is another ability that could really put a cramp on enemy strategies, but Bibarel's lack of overall durability hampers Unaware's effectiveness. I prefer Simple, but base this on your build.
Moody: At the end of each turn, one of the pokemon's stats is randomly raised by two stages while another is lowered by one. Moody has the potential to be useful, but it could just as easily cripple your Bibarel. I don't recommend it. This is a hidden ability.
You can try to turn Bibarel into a tank if you want, but I find it wiser to stick with its high(er) stats and give it semi-sweeping capabilities. Your primary weapons here will be Surf and Return, both boosted by STAB into relatively hard-hitting moves. Beyond that, fill holes in your team's move lineup. Superpower is a decent choice if you're coming up against other normal-types, though you'll have to swap Bibarel out to restore its stats. Super Fang is fun for cutting health down to half with each successful bite, and can come in surprisingly handy under some circumstances. Last, consider Dig to get Bibarel out of harm's way for a turn. I also highly, highly recommend giving your Bibarel Thunder Wave. Yawn is a potential alternative to Thunder Wave, but it's not quite as good.
If you wind up with a Simple Bibarel you'll probably want to toss in at least one stat-boosting move. I prefer Curse for boosting Attack and Defense, though this will be at the detriment of your Speed. Consequently, Curse (and Simple in general) is better used by Bibarels with a more defensive leaning and high HP.
EV / Super Training
My preferred Bibarel focuses on Attack and Speed EVs to boost its killing potential. This thing is just too frail for its defenses to really come into play, and you'll want to be as offensively powerful as possible to kill enemies in a single hit (and this is unlikely anyway). If you are going to try to turn our Bibarel into a damage sponge, allocate 252 EVs into its HP and shove the rest into Attack. Regardless of the route you go, Special Attack should largely be ignored.
Catching a Bibarel
Both Bibarel and its predecessory Bidoof are available on Route 22, early in the game. You can find Bibarel constantly in the grass on the top section of the Route; alternatively, you can hunt down a Bibarel if you use Surf and Waterfall to reach the lower section of the Route, near the Chamber of Emptiness. I recommend sticking with a level one Bidoof with maxed EVs, as you need every stat point you can get with this thing.