A little more info would help a bunch. I don't care how good of a mechanic a person is, it's nearly impossible to diagnose a problem with the little information given. I guess what I'm saying is, don't bet the farm on the quick diagnoses given.
First off, has it always ran this way or is this something that started suddenly or gradually became worse? Does it run ok after it's warmed up? My first suspicion would be it's caused by a lean mixture.
If it started suddenly, then something has changed radically such as a malfunctioning cam chain tensioner that let the camshaft jump a tooth but it would run crappy all the time, hot or cold. Or a temperature sensor suddenly croaked and the engine thinks it or the air temperature is a lot warmer than it really is, which could make it run lean when cold but run better after the engine is warmed up. A vacuum line could have been pulled off when the plugs or filter was changed. this would make it run very lean at idle but not as bad at wider throttle openings. If the bike is a 4 cylinder, two of the spark plug wires could be on the wrong plugs and would cause the same symptoms, but it would run bad all the time, hot or cold.
If the problem came on gradually, this could be one of several fuel injection sensors that went bad or a bad throttle position sensor.
Other things may include a stuck ignition advance if it has a mechanical advance. Did you suddenly start using a fuel with ethanol? Most times ethanol makes uo no more than 10% of the fuel, but legally (at least in Missouri) can be up to 20%. Ethanol has less energy for the same volume and effectively leans out the mixture. If the bike was running very lean to start with, this little bit could be just enough to push it over the edge. If the new air filter is less restrictive it or the ethanol + filter could definately lean out the mixture too much.
If you need more help, email me.