I found this discussion back in 2014, I am having the exact thing happen with the bike I just purchased. Cleaned the bowls, first street bike I have owned 1998 GS500E. Bought just to learn to ride prior to buying new. Learning how to fix on my own what I am comfortable with and don't want to spen a whole lot yet. So I cleaned the bowls and replaced needles and gaskets, ran great. Sat for about a week and now I have this issue, please see link mine does the exact same thing when started and barely runs with choke on. http://youtu.be/5GWw33dwui0 I pulled the carb today blew out the bowls as there were a couple specs of gross gas that I thought I had gotten out but it did not fix the problem. It was running rich, have it set to 2 1/2 turns. I am frustrated please help. Look to be honest I am no mechanic, but understand and have always worked on my own cars...had to. Yes I am a chick and by no means a young one (grew up in the 80's is as far as I will say) but I am damned determined to do this on my own if I can. I don't have specialized tools, Don't have calipers but can get a cheap pair and read them. Worked in quality control. Can someone please tell me what the hell and how to fix it or if its not worth fixing. Like I said after I cleaned the bowls it ran great the couple of times I or my husband took it out now this....I just want the damn thing to run maybe until I have to put it up for winter so I can graduate to a new one. I have never owned my own,  never rode one but as passenger but I can and will do this with a little help!! Thanks ahead of time!!!

You have fuel leaking from the exhaust port ?  Usually a overflowing carb will leak from the air box side long before the exhaust port. Is it gas or oil ? 2 completely different problems. 1 week after you cleaned the carbs and worked great means you have a non carb issue. Makes me think its oil. 1 week isn't enough to cause gas to go bad and gum up the carbs.
Cool.
Buddha.

It is definitely gas, I had the other issue first, I took the carbs back off there is still some small small specks of that old gas in a couple areas. I also notice the choke slide was bent some and one of the plastic holders that hold a gasket in I beleive had actually gotten pushed out. Not sure if that would have an effect or not. I had chainged the oil previosly because gas had gotten in when it flooded the first time and leaked all night. Also because there was so much gunk I don't think one of the main jets had gotten screwed all the way in as I was afraid of going to far. When I put it back together and put the pilot screw back in I with back it out 2.5 or should I go out more? Thanks for the response it is greatly appriciated, nice to be able to ask someone!!

Also prior to becoming a member I had read some of your responses and it has helped me out a bunch to begin with. I am winging it on most everything, I am pretty sure it was running a little rich prior to this time.
Sabrina

Hello Sabrina, and welcome

The bike in the video looked like a main jet fell out and it was running on the pilot. If your main jet was loose...

If the carbs are really dirty from sitting and full of dried gas-goo you can strip them down and soak the bodies/bowls/jets
in a solvent tank. I use mineral spirits in an ice cream bucket. The mineral spirits are oily and don't harm the rubber gaskets
or o-rings. (and you can reuse the solvent several times.)

Leave them in the tank overnight. After that you can clean with carb cleaner the regular way.

Having access to compressed air is almost essential to blow out the jets and carb passages; but if you don't have a compressor handy,
those cans of compressed gas for cleaning computer boards work pretty well. I get them at the dollar store for a few bucks each.

Don't poke wires etc. through the jets--even a small scratch will render the jet number meaningless. If the jet intakes have been gouged/stripped
by using the wrong size slot-screwdriver, replace them for the same reason: who knows what they really flow now?

Also. check your oil for fuel smell. You need to change the oil if it was contaminated.

Welcome to the forum, can you post a picture of the leak ?

How does the gas tank look, if the carbs were that bad maybe the tank is letting gunge through, although there is a little filter sock on the petcock.

Hello and thank you, I have taken the carb back off cleaned again for any small particles that I had missed the first time. Its back running but I am pretty sure gas has gotten into the oil, enough to smell in the dipstick, the oil is brand new so the viscosity and appearance hasn't changed a lot. The bike is now smoking after it warms up from the tail pipe. It was very bad at first but has gotten better after a while. I haven't rode yet for fear of getting stuck or damaging it. I also cleaned the airfilter as well as I could. Another thing now though I started it up on choke as usual and it idled ok without the air filter attached but as soon as I put it on it dies again. If I am right this means I need to adjust the pilot screw any advise on that? I will be changing the oil once again unless there is a way around that without causing an issue. I just want to ride before the weather turns bad, sux to have to ride Buddha Loves You when you have your own, not to mention at my age this is my best chance of getting good and comfortable to enjoy it!! Thanx guys for all the help you just don't know how nice it is!!!