If you Charter a bus is that bus considered a Common Carrier?

No. By definition a common carrier is an individual, a company, or a public utility (such as municipal buses) which is in the regular business of transporting people and/or freight. This is distinguished from a private carrier which only transports occasionally or as a one-time-only event. A bus 'chartered' to transport people is doing so as a 'private carrier'.

Another View: (in the US) Yes, and no, to the above answer. 'Common carrier' in this instance means that the coach operator holds itself out to supply transportation to the general public under licenses granted by the DOT and the ICC to perform service as a common carrier. Even though the chartered coach itself may not be involved in working a commuter route (for instance) it must still be operated by a common-carrier company.