On my 40 Ocean we had to lift the boat as high as the travelift could go and just barely got the rudder out that way. But our boat has a very long rudder shaft that goes all the way to deck level. I don't know which Bavaria 44 you have exactly. Many, but not all of the aft cockpit ones have a much shorter shaft. But likely you'll need to lift it too. Many boatyards are opposed to digging a deep hole in the ground below the rudder, which is the other alternative.
You cannot change the bearing or the housing without removing the rudder entirely, it's got to come out. "some cm" sounds pretty serious, so I wouldn't go sail until then. Let us know what you find - changing the bearing is fairly straightforward, but if the housing is broken too, that's encased in a big lump of fibreglass and a fair bit of work to cut out and install a new one.