If there's water water in the gas from condensation, it will sink to the bottom of the float bowl, since it's heavier than gas. Removed the float bowl and dump the gas (most Mikuni floatbowls have a drain spigot with a phillips head open/close screw, which is convenient, but you may have a Keihin carb).
With the float bowl removed, you have access to the low speed jet. Refer to you service manual (you DO have one, right?) to know which one is the low speed jet and which is the main jet.
Gently unscrew the low speed jet and clean the jet with spray carb cleaner and a soft toothbrush. Before replacing, remove the top cap from the carb and lift out the vacuum diaphram and slide and jet needle, since you may have crud on the needle. Reassemble carefully, making sure you don't pinch the diaphram. Do not overtighten the soft brass jet when reinstalling.
Shoot a lot of carb cleaner down the throat, aiming at all the little orifices (not at the manifold –– your pistons don't need cleaning). Then let it sit for a few hours. Hit the starter button and see what happens when the bike warms up and you turn off the choke.
Gas doesn't seem to be as clean or sediment-free as in the old days, but that may be the old fart in me speaking. Running a gas tank to very near empty is a good way to suck gas sludge into your carb, since all that crap settles at the bottom of the tank. I got stranded in the middle of nowhere on a vintage BMW by riding to the very bottom of the gas tank (no inline fuel filters). But taking two carbs apart and cleaning out the red slime is only a 20-minute job on an old Beemer.
You could take your bike to the dealer, but why pay someone else to do what you are perfectly capable of doing? Give it a try. Fixing it yourself isn't that hard, and it's a lot cheaper.