There are lots of issues using a B4 lens on the BMCC.
Crop factor is one:
Cheap adapters can let you down with flange distance inaccuracy.
There is the notion that B4's are made for triple CCD sensors and focus the 3 component colours, RG&B at different depths to counter registration errors due to the dichroic mirrors.
I believe that the small sensor and long flange distance of the 2/3" necessitated chromatic aberration compensation by splitting the difference between red & blue and focusing at the green (middle)wavelength to offset the CA.
There is a very expensive ($5000) adapter reputed to offset CA optically.
As for reducing F stops, many B4's are very fast to start with and can cope with 1 or 2 stops loss.
Info here could help though it is for B4 - M43's:
https://www.facebook.com/groups/B4onM43/I have ordered a B4-M43 adapter from a Polish guy who sells on ebay and also from his own site:
http://en.foto-akcesoria.com.pl/index.php/kategoria/35/canon-eos-adaptersI'm planning on trying my B4 on the Pocket Cam when I get it.
I thought of buying one of the Polish adapters as well as a 1.4 teleconverter for use on the 4K when I get mine but the use of B4's on large sensors does not work so well I believe..
They do better on smaller sensors.
Many are using them on GH2's etc.
There is a rumour that Metabones is working on an adapter.
A B4-M43 Speedbooster would be a dream.