One of my favourite stunts to pull when bear tanking is battle rezzing someone in the middle of a fight. It's clearly insane to do, but most boss fights have brief moments where you can get the 2-3.5 seconds required to cast Rebirth and get back into bear form. And while it's dangerous, I've never once died doing it. I have saved us from a wipe several times.
Yesterday in a Zul'Aman run I battle rezzed three times while main tanking bosses. First was on the Lynx boss. My pally tank partner taunted him off me in the joined phase and I did a quick Barkskin/Rebirth/Bear cycle. I ate one Saberlash which got me down to 200 HP so that was a close call, but we needed our priest. Second BR was on the Dragonhawk. That one's easy; when he's throwing bombs you have plenty of time to get off Rebirth, just be sure to warn your friend not to accept the rez until the bombs explode. The final BR was on the Hex Lord. We were halfway to a wipe but I thought we still had a chance, so I waited for him to channel his little shadow bolts and then cast a Rebirth. I forgot the Barkskin that time so it took awhile, but it got done.
I like to be aggressive on battle rezzes, using it the moment it looks useful. It's only a 20 minute cooldown, I've almost never had a problem where it was on cooldown when I needed it on another boss attempt. My guild's raid leaders are pretty conservative about using battle rez so right now it often goes unused. It's hard to optimize opportunity cost.
Some tips for battle rezzes while tanking... Use whatever dodge trinkets you have before shifting to do the rez, they'll help you in caster form too. Put Rebirth on your feral toolbar so it's a single click to shift and cast it. Generally it's not worth it to Barkskin before casting Rebirth; the extra 1.5 seconds GCD isn't worth the 20% damage reduction unless you also need the pushback resistance. Finally, don't get caught without mana after the cast; Rebirth takes 68% of your base mana which is probably pretty close to 68% of your bear suit mana, too. Make sure you have mana potions.