A little history.  I bought this bike for my wife for next to nothing.  It was in pretty rough shape when I got it.  It did run, but not well as it had been sitting.  It is a 2002, but has the 2004+ carbs on it (from what I gather, the 2001 and 2002 it was a toss up if it came with the old or new carbs).  As far as the motor/carbs/fuel goes, I cleaned and rebuilt the carbs.  I added the V&H exhaust and re-jetted the carbs.  If memory serves me correctly, I went with the 140 main jet, 22.5 pilot jet, left the main mid jet stock, set the float level to 14mm, and the fuel/air screw 2.5 turns out.  I also added a drop in K&N filter w/o the restrictor.  It runs really well now.  Its got good throttle response and pulls very well through all rpms and gears for only being a 500.  The only issue I have is that the choke doesn't seem to work.  Physically speaking, all of the mechanical components of the choke work, but if I try to start the bike using the choke, it won't start.  Not using the choke, I can start the bike fine and just keep it idling around 2k rpm manually with the throttle for a few minutes and once its warm, its golden.  If I try to use the choke once its started and I'm warming it up, it will die.

Its not a big deal being that I live in TX, it warms up in a minute or two, but since it's my wife's bike and she's just learning, I'd like to keep things as simple as possible.  Being able to set the choke, start the bike, and let it warm by itself would probably help out some.  At this point, I'm not really even sure where to start with this issue.

And since everyone likes pictures, here are some of the finished project, I only wish I took some of when I got it.  It was pretty trashed, but next to free.  Like mentioned above, K&N filter, V&H exhaust, rejet carbs, racetech springs with 15w fork oil and new seals, Katana 600 rear shock, new brakes and fluid all the way around, new bars, bar end mirror, and I think that's about it off the top of my head.

With the bike cold and running, will setting the choke kill it instantly? Or do the the revs hold, raise then drop, or slowly drop etc?

Just went to the garage to check and the battery is dead.     The one thing I forgot to replace.  I put it on the charger, but if I remember correctly, I get it started, keep it idling high, and if I try to choke it, it will stay running shortly and start to die like it is being starved of fuel.  It never revs up like you would normally expect from a choke.

Battery charged enough to start it.  Once running and idling it manually around 2k to warm it up, if you try and choke it, it pretty much kills it immediately.  Though it didn't run great when I got it, it was all stock and it acted the same way.  The choke just wanted to kill it if it was running cold and didn't want to start if you were trying to choke it cold.

Like previously mentioned, once warm, it idles great wherever you set the idle and it seems to be running spot on (not lean or rich).  It's just a bit of a chore getting it warmed up.

my choke does absolutely nothing as well. It actually lowers the rpms instead of raising them. I've cleaned my carbs thoroughly a number of times and it still doesn't work. I have to turn up the idle when I start it, and keep lowering it as the bike warms. Big hassle, I'll figure it out eventually, I hope.

I've found that too much choke is bad especially in warm weather.  I generally do not use over half choke for starting unless it is very cold out.  With full choke mine will fire and then die immediately and not fire again until i take off at least half choke.  It is pretty easy to over do it with the choke especially in the warm, but the choke needs to be that way so that it can start when it is below freezing out.  I have always considered this normal.  It will not run any better with too much fuel than with too little.  There is always a sweet spot for the engine temp.

Idling to warm up seems to take longer than riding.  I usually use just enough choke to hold it at about 1.5k to 2k (normal idle at 1.2k) and ride for a few blocks before it is ready to run with the choke off without bogging.  Warming up idling seems to take at least several minutes

Maybe someday I need to go out and just try starting it with the choke at various spots. I feel like if that was my problem I would've figured it out by now, but who knows. I'm always afraid of killing the battery before I get the bike started so I just go with adjusting the idle, which I know works, but it's worth a shot.

Died on choke = clogged pilot jet. Choke sucks through the pilots. Split and clean it. While you in there jet it too.
Cool.
Buddha.

Not sure if you read my post, but I just recently cleaned and jetted them.

I've thoroughly cleaned mine a number of times as well and it never changes. I actually have a second set of carbs now and i'm going to try soaking the whole setup in a couple bottles of pinesol for a day or two and try the other set, see if it helps.

pinesol? thats about as weird as the airbrushers who swear by thinning down paint with windex

Don't people usually soak stuff in kerosene?

Haha, I don't know, it was someone's idea on here. It's a happy medium between things too harsh for the plastic/rubber fittings on the carb, and something too friendly to actually clean anything. He posted pictures, he just filled a container with 3 bottles of it, set the carb in for 24 hours, and it looked like a whole new set of carbs.