Thinking of making PR for this in near future but first I want to know if it would be accepted. @pierredup

I would copy contents of https://github.com/Payum/Payum/tree/master/src/Payum/Core/Bridge/Symfony into root of https://github.com/Payum/PayumBundle fixed namespaces and references inside of PayumBundle. Next would be tests from https://github.com/Payum/Payum/tree/master/src/Payum/Core/Tests/Bridge/Symfony.
That would be all needed to do in PayumBundle PR.

What I'm not completely sure what to do in Payum/Core to keep it BC.
Maybe replacing contents of all classes with extend to PayumBundle's version?

Is there better solution than this?

<?php
// src/Payum/Core/Bridge/Symfony/ReplyToSymfonyResponseConverter.php

namespace Payum\Core\Bridge\Symfony;

if (class_exists('Payum\Bundle\PayumBundle\ReplyToSymfonyResponseConverter')) {
  class ReplyToSymfonyResponseConverter extends Payum\Bundle\PayumBundle\ReplyToSymfonyResponseConverter {}
} else {
  class ReplyToSymfonyResponseConverter {
    // original content of the class
  }
}

@Tetragramat I think in payum/core, the classes can just be deprecated with a message specifying to use the classes in the bundle instead.