I want to reduce outbound traffic cost from S3 bucket to internet

With CloudFront, you get extra benefits in addition to better Data Transfer rates, in terms performance, security and serving of your traffic closer to your users; and you can also save up to 30% additionally with the Savings Bundle - https://aws.amazon.com/cloudfront/faqs/#CloudFront_Security_Savings_Bundle - it's a similar concept like Reserved Instances or Savings Plans, if you commit to a certa amount of traffic for 1yr.

Additionally, check the CloudFront pricing page here - https://aws.amazon.com/cloudfront/pricing/ - regarding possibility to commit to a private pricing rate if your monthly usage is at least 10Tb (which I understand it its...) which will likely give you even better discount than Savings Bundle in return for a commitment certain amount of usage usually, for 1yr time. You would generally discuss it with your AWS account manager, or if you don't know them - you can fill in the Contact Us form (link provided on the pricing page).