I will be flying into Chengdu Airport. Is there a Shuttle Bus into the CBD please?

May I know whether the CBD you are referring to is near local East Street area? If so, I suggest you take airport shuttle bus line 2 to Tianfu Square, near which you can transfer to subway line 2 to get off at Chunxi Road. Then you can easily walk to the destination. If not, just show me more details and I will help!