The first thing you should notice and keep a track off is your subdomain name must be the same as the S3 bucket name.
Once you name a new bucket as per your Sub Domain naming convention, you will have S3 URL assigned to it that looks something like http://subdomain.domain.com.s3-website-us-east-1.amazonaws.com
Now Next thing you need to do is to host your domain and map your subdomain to the URL from above step. where a mapping the host "subdomain" to the address "subdomain.mydomain.com.s3-website-us-east-1.amazonaws.com" as a CNAME record.