Sounds like you may have some debris in your float valves. I'd recommend attaching a suitably sized hose to the nipples of each float bowl, draining each bowl into a cup (so you can see any debris that is flushed out), then flipping your petcock to the 'on' position for a few seconds with the drain still open to flush fuel through that float bowl, possibly unseating some debris. Repeat for the other three float bowls.
Then fire her up and if she runs OK, see how she does/take a short trip. If you still smell fuel after you take a short ride, you still have a problem. Otherwise, problem solved for now.
Where you are smelling fuel, don't ever leave your petcock in the 'on' position, as some fuel may get into the cylinder, and cause a hydrolock. The 'run' position (the one that flips on when the vacuum picks up) is probably OK, but as Connie petcocks age these can fail...
If you have fuel seeping into your air filter, btw, you are running a huge risk of hydrolock...
Search for hydrolock on this board if you need more info about what this is. Essentially, a cylinder fills with fuel, then when you try to start the bike you end up bending a rod (fuel has nowhere to go and won't compress) and damaging the engine. It doesn't happen often, but Connie owners need to be vigilant with carb and petcock maintenance else you run the risk of this happening.
Back on topic, if the 'flushing the float bowls' trick doesn't solve your issue, it's time for a carb cleaning/rebuild. While you probably can do a somewhat good job yourself, the collective here recommends that you get in touch with Steve In Sunny Florida/Shoodabeen Engineering. He specializes in Connie carbs, and will do you right! Plus he has some economy & performance upgrades that might intrerest you...
Your local bike shop will probably charge you a lot more than Steve will, and may end up not doing the highest quality work...
Also, his overflow tubes are a very nice option to prevent/protect against hydrolock.
www.shoodabenengineering.com/All of the above said, take a few minutes to inspect your vacuum lines and fuel lines. A pinhole in a fuel line, or an improperly attached one, could also be releasing droplets of fuel. Just trying to think of all the bases here.