You need to use a combination of [turn:lanes](http://wiki.openstreetmap.org/wiki/Key:turn) and [change:lanes](http://wiki.openstreetmap.org/wiki/Proposed_features/change).
I think something like
turn:lanes=through|through;right
On the Ferdinánd híd from left to right (from the point where there is a half circle to the north)
<pre>
lanes=4
lanes:forward=2
lanes:backward=2
change:lanes:backward=no|no
change:lanes:forward=only_right|yes
turn:lanes:backward=through|through;slight_right
</pre>
then the section between the entrance from the west and the exit towards the parking
<pre>
lanes=5
lanes:forward=2
lanes:backward=3
change:lanes:backward=no|yes|no
change:lanes:forward=...
turn:lanes:backward=through|through;slight_right|slight_right
</pre>
perhaps you could add a destination:lanes:backward=||parking as well
after the exit to the parking
<pre>
lanes=4
lanes:forward=2
lanes:backward=2
change:lanes:forward=only_right|yes
change:lanes:backward=only_right|yes
</pre>
for the "turn" from the west
<pre>
lanes=2
change:lanes=no|no
lanes=2
all turn:lanes=through|right
</pre>
One can discuss about that last turn:lanes, since but are turning to the right.
OsmAnd understands turn:lanes, but not change:lanes
I have to admit that I used some information of these Google StreetView to write the above, since the Bing images are not veyr high quality. I know I am not supposed to do that and hope you have to be suffixed with :forward or :backward in case it's a not a oneway way.
I might take another local knowledge to properly map the situation without the need to look at it later on (if no better answer is provided in the meantime), but right now I don't see how the map relates to the photo in Google Streetview
StreetView.
