Yes, you can. On the Enterprise tier plans, you can connect your own S3 bucket. This bucket will then be used for image storage instead of the Bannerbear default CDN.
To activate this feature, go to your Project and navigate to:
Settings > Advanced → > Custom S3 Settings
You will need to provide the following:
It is highly recommended that you create a new IAM user with very limited permissions, for this purpose. The only permissions the user needs are putObject and putObjectAcl on the specific bucket that you intend to use. Here is a sample policy you can use as reference ↗.