Have not tried to PvP with the above macro, but it was made with a PvP intent.
The Rake uptime is perfect, while the Rip is slightly clipped.
In practice, Rake might not be up 100% of the time, but Rip should be.

I took the Tiger's Fury, /Use 13 and /Use 14 out of the standard macro, as they augment the Rip which then cannot be reapplied once the buffs fall off.
The basic choice is to include that in the macro, and write it so that you Ferocious Bite after the first Rip... or to take those out of the spammed macro and save them for when you'd like to apply burst/pressure.
The extra 60 energy portion of the Tiger's Fury is wasted on the opening press, if it is included in the base macro, but not having to manage the ability is a bonus too.

I'll definitely want to be Hit capped for PvP content, as the 20% chance per combo point (with any finisher) to make a Nature spell instant, is fairly important.
With four or five combo points on the target, there's a very high chance (just over 97%, for my crit level) for the next Nature Spell to be instant.
Not sure if Expertise Rating is worth going for; chances are, I'll not gem/enchant for it but not reforge out of it either.

I haven't done anything for PvP as a Bear, per se. I do have two-step mapped keys, which will shapechange a given toon into Bear Form, so they can be shifted individually.
In addition, there are keys for everyone into: Aquatic, Bear, Cat, Flight and Travel form.
I've heard Bear Form survivability is great, with cooldowns... and that Vengeance is quite possibly overpowered in PvP.
Bear would likely want to mostly Mangle, especially with Berserk if that was available.

I've been manually using: (Key A) Feral Charge - Kitty; and (Key B) Ravage.
They don't combine too well into a macro for some reason.
A two step mapped key will probably be superior.
I'm also thinking of using, in the place of Key B:
#show Ravage
/cast [stealth] Pounce; Ravage

I have a macro, which I've placed on a thumb button (one is FTL Follow, the other is this macro):
#show Prowl
/cast [nostance:3] Cat Form; Prowl