I can tell you what the problem is Guaranteed!. So please attempt to try my option out .
Every single Suzuki I have ever owned has done the exact same thing . Suzuki are cold hearted women . PERIOD.
So what you do is start it with the choke on . Leave the choke on for a while. After about 5 or 10 minutes , the engine will start to Rev and Rev and Rev until it's almost redlining. Then and only then take or turn your choke off . If it's a lever that you pull up , you may have to lightly tap it down a hair at a time . Like tap , revs lower but stays running , tap again , lowers Rev etc. Until it's off and it stays running and idles with no choke or throttle . Then you can take off , shifting and giving it throttle . If the doing the steps does not allow it to idle on its own , adjust your idle screw so it does. Suzuki carbs are ULTRA ULTRA sensitive with this adjustment , so it may not run with a quarter turn left or right , but it will at an Eighth of a turn . So don't give up , it just takes a while , but once you get that idle screw perfect, Don't ever touch it again EVER. Then you only have to deal with the choke. This is the way all Suzukis are engineered to work . Trust me . Although every post on here has good intentions , I guarantee you success . Good luck my brother.