Not sure if it's enough with Warrior's insane healing with Second Wind, but try going stealth to force him to grab one of the 5% damage taken debuff/see stealth purple crystals. As soon as he grabs one, Feral Charge, and hit all your openers.
Also, I haven't tried this, and I'm not sure how practical it really is, but it may be worthwhile to attempt a combo with Heart of the Wild + Bear form after you get all your Cat form bleeds up. I mean to try this against a training dummy tonight before the arena reset tomorrow, to see if it is actually a burst increase.
EDIT: I'm assuming you're at the end of a match and it's 1 vs 1, you and the Warrior.
It's really not that practical. Everyone complains about druid mobility sure, but how long does it take us to get AWAY from that shockwaving double charging heroic leaping safeguarding warrior so we can actually do it, just to have that 55k casted healing touch and the ~25-30k healing from rejuv be taken away in seconds?
Also, letting a warrior get shadow sight won't matter, it'll just hurt you in the long run unless you somehow magically get an opener on him from the side of a pillar before he charges/shockwaves/leaps.
Our bleeds tick for decent amounts if TF/Trink'd (~30k+ rip tick crits) however it's simply not enough to damage through second wind with the CC also available.
It's really not practical to kill a similarly geared/skilled warrior 1v1 as a feral without cooldowns, under 35% a warrior with that kind of gear will be regenning 6-7k HP a second. If you don't think you can outlast him until then however (his cooldowns will likely come back as well) push him down to (and try to keep him around) ~35% or 40% with use of Tiger's Fury and bleed kiting, making sure to keep yourself healed and then wait for your stun DR to come up.
Once it does make sure you have bleeds up and then bash and tear into him with whatever you have. If it's not enough; cyclone him to stop the heals and the CC a bit while your energy regens and then reopen on him with the rest of what you've got. If he's got wall/cry/parry crap he just made your life even more miserable, and will most likely force you to have to wait on DRs again.
Warriors, while not on the level of frost mages last season, are one of the most annoying classes for us to try to kill 1v1 right now, so don't expect to always win against good ones. The amount of CC they can stop your burst with (especially 20s shockwaves...) is insane, so don't get too discouraged.
TL;DR: Outlast til about 40% and then go to ham town on them, using clone to stop second wind heals if needed, not a fun or easy fight but possible.