If i arrive at 300AM in Taipe Airport is there a bus that can take me Taichung?

Do you mean the Taoyuan International Airport? I'm afraid there is no bus to Taichung operating at that time. You are advised to take the airport shuttle bus no.1819 to Taipei Railway Station, and have a rest in a nearby hotel. You may head for Taichung next morning. The Rose Boutique Hotel Taipei Zhanqian Shop may be a nice choice. It is located at no.3, Huayin Street, which is only 330 yards (300 meters) from the station. The standard room may charge CNY350-400.