Running your own registry is not the only way to have a secure, private store for image repositories, there are several third-party offerings you can use. In practice they all work in the same way - you need to tag your images with the registry domain and authenticate with the registry server. There are several options available, and the most comprehensive ones come from Docker, Inc, which has different products available for different levels of service.
Docker Hub is the most widely used public container registry, averaging one billion image pulls per month at the time of writing. You can host unlimited public repositories on the Hub and pay a subscription to host multiple private repositories.
Docker Hub has an automated build system, so you can link image repositories to source code repositories in GitHub or BitBucket, and Docker's servers will build an image from the Dockerfile in the repository whenever you push changes - it's a simple and effective...