The nearby late M star Gliese 569B was recently found by adaptive optics imaging to be a double with separation \sim 1 AU . To explore the orbital motion and masses , we have undertaken a high resolution ( \sim 0 \farcs 05 ) astrometric study . Images were obtained over 1.5 years with bispectrum speckle interferometry at the 6.5m MMT and 6m SAO telescopes . Our data show motion corresponding to more than half the orbital period , and constrain the total mass to be > 0.115 M _ { \odot } , with a most probable value of 0.145 M _ { \odot } . Higher masses can not be excluded without more extended observations , but from statistical analysis we find an 80 % probability that the total mass is less than 0.21 M _ { \odot } . An infrared spectrum of the blended B double obtained with the MMT has been modeled as a blend of two different spectral types , chosen to be consistent with the measured J and K band brightness difference of a factor \sim 2 . The blended fit is not nearly as good as that to a pure M8.5+ template . Therefore we hypothesize that the brighter component likely has two unresolved components with near equal masses , each the same as the fainter component . If Gl 569B is a triple our dynamical limits suggest each component has a mass of 50 ^ { +23 } _ { -4 } M _ { jup } . We infer an age for the system of 300 Myr , from its kinematic motion which places its as a member of the Ursa Major moving group . All the above parameters are consistent with the latest DUSTY evolutiuon models for brown dwarfs .