Below are AWS CLI commands that can be used for quickly determining the current size of an S3 bucket.
aws s3 ls s3://[bucket_name] --recursive | awk 'BEGIN {total=0}{total+=$3}END{print total/1024/1024" MB"}'
aws s3 ls s3://[bucket_name] --recursive | awk 'BEGIN {total=0}{total+=$3}END{print total/1024/1024/1024" GB"}'
aws s3 ls s3://[bucket_name] --recursive | awk 'BEGIN {total=0}{total+=$3}END{print total/1024/1024/1024/1024" TB"}'