  We perform a study of the $B^{*+}B^0,B^{*0}B^+$ correlation functions using
an extension of the local hidden gauge approach which provides the interaction
from the exchange of light vector mesons and gives rise to a bound state of
these components in $I=0$ with a binding energy of about $21$~MeV. After that,
we face the inverse problem of determining the low energy observables,
scattering length and effective range for each channel, the possible existence
of a bound state, and, if found, the couplings of such a state to each
$B^{*+}B^0,B^{*0}B^+$ component as well as the molecular probabilities of each
of the channels. We use the bootstrap method to determine these magnitudes and
find that, with errors in the correlation function typical of present
experiments, we can determine all these magnitudes with acceptable precision.
In addition, the size of the source function of the experiment from where the
correlation functions are measured can be also determined with a high
precision.
