I don't think the 44 Bootes is an xray binary system. My understanding is that an xray binary is a main sequence star paired with either a neutron star or black hole, and that the accretion of matter from the main star to the neutron is creates a significant amount of xrays. 44 Bootes is three main-sequence stars.
Cygnus X-1 is about 8,000 LY away but I was wondering if that was the closest one.