(@aws-cdk/core): Hiding or Redirecting Docker Output

## :question: General Issue

### The Question

When using `BundlingDockerImage` or the new `DockerImage` classes, when the docker process fires up and runs commands within the chosen image, the output of those commands is piped to the terminal. I combed through the codebase but could not land on a method to hide the output, or pipe it to a different destination.

What's the preferred method for doing either?

### Environment

- **CDK CLI Version:** 1.95.1
- **Module Version:** n/a
- **Node.js Version:** 14.15.3
- **OS:** All
- **Language (Version):** 4.2.3

### Other information

Start by tracing the BundlingDockerImage and DockerImage entry points mentioned in the issue to find where Docker command output is handled. Determine whether the preferred behavior is suppression or redirection, and consider the work complete when that behavior is available through a clear, tested interface.

Written by the indexing model from the issue text.