I would inject free biotin after immobilizing the first biotinylated DNA strand. To make sure this is OK add one channel with only free biotin blocking all the streptavidin channels. That will leave two channels in the Biacore (2000/3000) to do the reverse experiment.
In our duplexes, both 5' extremes will be biotinylated, and can be fixed to the surface. We are interested in fixing only one of the 5' ends.
(I am new to this technique and went wrong in my last reply, sorry).