Alain,
I have used the Sansamp BDDI with 2 basses with Alembic pups (Jazz bass with Activators; 6-string fretless with AXY+Signature electronics).
Of course sound is very personal and writing about it is not a very objective process, but I just wanted to let you know that, although the BDDI does live up to its reputation (emulate a big tube amp's tone), I found it adds harmonics in certain frequency range that did not sound too pleasant to my ears (upper mids) and - more importantly - I found it impossible to tweak that character out of the sound, i.e. run it (close to) flat. I ended up selling it again for that reason and found myself using a Line6 Bass POD XT (Alembic F2B patch) to add a little tube edge without the frequency notch added (then again, the Line6 has its own particularities and does not run completely flat either).
Just my 2 cents. Take care, RR