I unwittingly deleted the CdkStack in CloudFormation, but re-running cdk bootstrap again resulted in an error telling me that the S3 bucket used by CDK already existed but wasn’t in my account.

This is because it may take up to an hour for a deleted S3 bucket name to become available to use again.

The AWS docs mention a --qualifier command line argument for cdk bootstrap, which by specifying a new qualifier, you can change the bucket name that is used:

cdk bootstrap --qualifier MYQUALIFIER

The custom qualifier must be all alphanumeric and no more than 10 characters.

The bootstrapQualifier property in the cdk.json file also needs modified:

{
  "app": "...",
  "context": {
    "@aws-cdk/core:bootstrapQualifier": "MYQUALIFIER"
  }
}