I'm not sure this is the problem but my bike will do this on occasion. The fix is in resetting the idle position for the throttle cable. To do this, you switch the ignition off and on three times, allowing the fuel pump to bring the system to pressure each time. Then it will function as it should. Leave the kill switch in the "on" position when doing this. Hope it helps you.

 

Went through this exact problem with my 2007 Softail Custom.

Replaced IAC, and some other sensor.

However, the culprit turned out to be the VSS (Vehicle Speed Sensor).

An unlikely candidate, but that was the fix.