trigger command on registry update
The key words here are:


  Pipeline on Bitbucket


You already have a pipeline. This is where you would stick the deployment command. 

AFAIK there is no standard tooling for registries to 'push out' any changes; you'd have to code a custom integrator that continually polls for changes and compares. This would be a lot of work. Same goes for having your servers directly listen for changes on the registry.

It would be far easiest (and is the standard) to simply have your build pipeline issue the deployment command after its successfully pushed a new image to the registry. 

There are benefits to this: 


your pipeline is aware of whether the push to the registry failed or passed (and you can handle that failure gracefully with retries)
your pipeline will be aware of the new registry tag
your pipeline can control exactly which tag gets pushed where, when, and how quickly
your pipeline has the same insight to whether the deployment passed or failed, and can attempt retries or perform notifications of failure