Hi Gildas-
You can find my version of the LaTeX bundle here:
http://vze26m98.net/tm2/Biber%20LaTeX%20bundle.zip
As I said, I updated work I did on 1.5 and it seems to work in TM2.
As with your modifications, all it does is update latexmk.pl to a recent version (4.23a) and add some functions that will put Biber's messaging into the HTML output window. It may not fix all of your (or others) issues with the bundle.
I also put my .latexmkrc file in the ZIP above, to illustrate how I get latexmk.pl to run Biber and XeLaTeX.
Specifics:
. The bundle modifies the most recent "Managed Bundle" for TM2 (a/o 12/14/2011) . I installed it by making a modification to the managed LaTeX bundle, and then copying my bundle over the bundle created in the Avian folder. . My bundle modifies: texparser.py (mostly) and LaTeX and View.plist (slightly). That's it. . It updates latexmk.pl to v4.23a
I'm busy with semester end right now, so support may be slow or limited until 12/20.
And again, I have no idea whether this constitutes a fix/work around for others having issues with the LaTeX bundle on TM2.
Keep me posted!
Charles