You said that a little gas came out of the petcock? I am assuming you had the fuel hose off the bottom and it was not a steady stream? If this is the case the problem is in the tank either the vent hose is clogged or the petcock screen is clogged like has already been said.
With the hose off the petcock take the gas cap off, if gas starts to flow it is the vent hose, if not it is the petcock or screen.
If I am reading your post wrong and you did have a good stream of gas out of the petcock the fuel filter is clogged or your fuel pump is bad. When you turn your ignition switch on you should hear the fuel pump click for a couple of seconds if no clicking the pump is most likely bad.
The reason your bike started after sitting is because some fuel is getting by and filling the bowls but you are running it out before they can refill.
You can also take the hose off at the carbs and see if you have good flow.
Here is a post for an alternative fuel pump, an OEM is a couple hundred bucks last time I checked.
http://www.venturerider.org/forum/showthread.php?86265-Mr-Gasket-Fuel-Pump-Conversion