I am just posting up an item build for now, will flesh it out in time.
You are already expected to know how to play Volibear.
This build focuses on getting the bloodrazor after warmogs for dps. because its inherent damage, armor, plus the atkspeed is better than getting the atmas right after warmogs.
Rushing Hp early on on volibear is strong, it meshes well with his passive and is overall a good choice. but after that, to keep stacking hp "because it synergies with his passive" is a bad idea because it leaves you with a no resist, and a complete lack of damage.
what a balanced build should do is account for all of his strengths and weaknesses.
WARMOGS - what warmogs does is provide that pool of HP from where Volibear's abilities benefit.
now that we have HP taken care of we need some resist and damage.
BLOODRAZOR - the perfect combination of armor, dmg, and atk speed. the armor will make him less squishy, the damage is always welcome. and the atk speed will improve his FRENZY
Now that our CORE is finished, we have to build on it or "improve it". HOW?
WELL, 2 good choices ( based on the enemy teams comp) are ATMAS and BANSHEES
ATMAS - improves armor and dmg
BANSHEES - improves magic resist and HP pool
theses are good items but dont scale very well into late game, and slow down your overall build, therefore are optional.