After some poking into the SecurityBundle of Symfony itself, I figured out the following:
Given this is in your security.yml:
providers:
AdministrationUser:
entity:
class: AdministrationBundle\Entity\User
Symfony will create a service with the following name:
security.user.provider.concrete.administrationuser
This service uses the UserProviderInterface and when you fetch this service you can simply call the method loadUserByName and find your user.
So all you need to know is the name of the provider you configured yourself and you can determine the service-name and fetch it.
I'm in a more generic situation, so I added an alias to that service in the Extension-class of my bundle:
// alias the user_provider mentioned
$container->setAlias('my_security_bundle.user.provider', new Alias('security.user.provider.concrete.' . strtolower($config['user']['provider'])));
Where $config['user']['provider'] comes from config.yml (and needs to be configured in your Configuration class, but that is a different story.
Now I can simply use that new alias and I will get the correct service to find my user in a Controller like so:
/** @var UserProviderInterface $userProvider */
$userProvider = $this->get('my_security_bundle.user.provider');
$user = $userProvider->loadUserByUsername('someone@somewhere.tld');