AWS S3 Bucket with Multiple Regions

You're looking for Cross-Region Replication:
Blog Post
AWS Documentation

Cross Region Replication allows for the automatic and asynchronous copying of your objects between S3 buckets in different regions.

An S3 bucket exists in one region, not in multiple regions, but you can access that bucket from anywhere.

Now, while you can access a US Standard bucket quite happily from Singapore, the latency will be high so you might want to consider using CloudFront as a CDN.