Choke on a suzuki gs1100 gk /mikuni 34mm carbs

That bike has 4) 36mm Mikuni carbs. Most likely they are stopped up. If you have been running U.S. Fuel with ethanol added this is not good for the carbs. Or most likely it was sitting for the winter, and the carbs got stopped up. If you have the carbs cleaned out, this will fix your problem. Keep me updated, and good luck. P.S. if a shop does this work it will be expensive, its not a hard job just time consuming.

Sounds like carbs need a good clean out. The 1991 model GSXR was not Electronic Fuel Injected. A model this old may also be subject to the carbs being worn out and letting in unmetered air around the screws etc, which may be keeping the revs up at idle and causing a lean idle.
Applying load will source fuel from the next jet and hide the problem. Applying choke holds back some air which will help as it sounds like too much air at idle. This will not help as much when bike is warm.
Bottom line is your carbs need a good clean and service and maybe if they are leaking air they might need to be replaced.

You may have a vacuum leak. Your carbs may just need be adjusted and synced. I would not be surprised if the carbs have been out of sync since day one.

Water in the carb float bowl? Remove the carb then remove the float bowl. Use spray carb cleaner to clean the carb. Pay special attention to the main jet.

Carburetors Mikuni

you may have to take the carbs off for a really good clean

Possibly the choke is getting stuck internally, Even thoug the leaver may be in the closed (normal) position, it may be sticking internally. Try removing the choke and cleaning the passage with some carb cleaner, then replace the lever. The bike could run with a partially cloged choke but would be tough to start when warm due to too much fuel. Another thing to check, when it is hard to start, just after kicking it over a few times, remove the spark plug and see if it is wet with gas. My guess is that's it's soaked. Good luck.

Sure it has choke? Could be injecter clogged

If yours is a Mikuni carb, here's what I did to make my choke work manually on a 1986 Plymouth Voyager:

http://imhdd.ms11.net/CHOKE/choke.html

sounds like the main jets are partly pluged, you must remve all brass jets and seats including needle jet and its slide soak in carb cleaner and blow out with compressed air only.. hold up to bright light to verify if all are clean. jim