How long does the bear form stay?
It has the same duration as your standart/whirlwind rage and uses your rage charges. But! It doesn't get any benefits from other rages, thus if you chose whirlwind frenzy, you won't get additional attack in bear shape as it's a separate feat.
With that said, what is a good bear warrior build?
It's a tough question, lol. What RagingPeace suggested is pretty simple, but works, although in BW builds there's no point to go for Barb20 as epic rage doesn't give any benefits in Bear shape, thus you can experiment. For example, I played Barb14/R3/WS3/BW10, thus gaining evasion, full umd and scent+swift tracker combo. As an option, you can also dip into bear warrior while using normal Barbarian rages. For example, Barb20/B-guard3/WS3/BW4 is a build I made up and it looks really solid, Bear warrior here gives you scent+swift tracker combo and free knockdown and extended rage feats.
A little bit more about how bear warrior works...
First off — your damage is going to be garbage ANYWAY, no matter how much you invest into strength, Bear warrior is a PvE tanking class. Still, there are ways to make it not-as-bad, thankfully non-physical damage from your weapon and unarmed strike feats transfer into bear shape. So:
1) Some weapon with elemental damage, the best choices are imho Jolt of lightning and Spectral dagger as they are cheap and give +1d6 non-physical damage that transfers into Bear shape, other weapon properties don't matter as they're overwritten with BW natural weapon.
2) Blades of fire wand or Perfected alchemical fire. +1d8 or +1d10 fire damage respectively. Duration itself is ridicolously low, BUT if used prior to shifting, it will maintain through the whole duration of your Bear shape which can be up to maybe 5 minutes with feats and Con.
3) Weapon of Frost wand. +1d8 cold damage, it will work strictly for its duration (3 minutes for a wand) unlike Blades of fire. Why not Flame weapon instead? Because it doesn't stack with other fire damage sources.
4) Unarmed strike feats. They all work in bear shape and transfer there, such as weapon focus, weapon specialization, improved critical etc. Moreover, feats given by items transfer as well, so gloves with Improved critical (unarmed) are really useful.
So with all abovementioned, you will additionally have +3d8 damage bonus atop of your basic damage which almost doubles BW's damage output, heh.
As for defensive part. You can read on the wiki what transfers and what doesn't to shapechanged armor. But basically, in epics your AC should be around 51-54 by default. Turn on ICE and you're reaching 60ish. All the dex transfers into Bear shape, so it lets you go much above that.
Poke me if you got questions here!