Sounds like you've either got an air leak, a clogged main jet, or a leaky needle valve.
According to this pic you've only really got two places to leak.
1) The o-ring between the carb and the head.
2) The o-ring where the top cap screws onto the top of the carb.
A quick test for this is to soak the two potential leak areas with WD-40. This will temporarily seal any tiny leaks, allowing you to start the bike more easily and let it run without the choke (which is actually a fuel enrichment on this bike, not a choke). If that works, replace the two o-rings and you're back in business. If not, you'll need to go inside.
If it were my bike I would remove the carb and clean it out. Don't settle to just squirt it with carb cleaner. Get a can of paint brush cleaner or a can of carb dip. Take the entire carb apart and soak everything for a few hours. This will dissolve all of the varnish, scale, old fuel, and any other crap in there. Take a tiny piece of wire and poke it through the main jet and any other orifices you can see. After that, blow backwards (from the bowl) through any other passages with compressed air to dislodge anything that might be in them. Put everything back together with a new carb kit and you'll be back in business. A new carb kit will only set you back about $12 from ebay. They usually come with parts to build a few different carb models, so be careful to pull the right parts out of your kit. The last ones I built came with three types of air screws, four main jets, two pilots, etc. All of the parts have their size etched on the side, so just make sure to keep track of what size you take out so you'll know what size to put back.
During disassembly be very careful with the needle valve assembly. They usually have a delicate felt washer between the needle seat (the part that looks like a hollow bolt) and the carb body. If you break the washer it will leak onto the ground forever.
The worst case is that you have a burned valve. This will cause low cylinder pressure, which can require the use of starter fluid when starting. Check the compression to see if this is the case.
Good luck. If you have any carb questions feel free to e-mail me.