Shouldn't really be necessary since CB is completely responsive and can just be viewed from the mobile browser. You'd miss out on push notifications unless you implemented the JS for those. You can reduce data usage by heavily compressing headers and using lazy loading for images; both doable using JCH Optimizer (we're using it here, works very well). Quickest solution is a small app that's just a wrapper for the website with maybe some custom client side caching of pages.

Is there a kind of bridge (xml or so) to be able to manage CB subscription, profile, messages and so on from a mobile app?

No, you would need to develop an extension or CB plugin to create a JSON endpoint API for handling all of your apps necessary requests.

I am just trying to not build from scratches a web service to read and write in CB database, because it would take a lot of time.

That's basically what you'll have to do. You can try using CB Auto Actions for the endpoints I suppose though and at least reduce some of the workload since it can do PHP output for any action type now you can handle JSON outputs for various action types.