The Milky Way Bulge extra-tidal star survey is a spectroscopic survey with the goal of identifying stripped globular cluster stars from inner Galaxy clusters. In this way, an indication of the fraction of metal-poor bulge stars that originated from globular clusters can be determined. We observed and analyzed stars in and around BH 261, an understudied globular cluster in the bulge. From seven giants within the tidal radius of the cluster, we measured an average heliocentric radial velocity of 〈RV〉 = −61 ± 2.6 km s−1 with a radial velocity dispersion of 〈σ〉 = 6.1 ± 1.9 km s−1. The large velocity dispersion may have arisen from tidal heating in the cluster’s orbit about the Galactic center, or because BH 261 has a high dynamical mass as well as a high mass-to-light ratio. From spectra of five giants, we measure an average metallicity of 〈[Fe/H]〉 = −1.1 ± 0.2 dex. We also spectroscopically confirm an RR Lyrae star in BH 261, which yields a distance to the cluster of 7.1 ± 0.4 kpc. Stars with 3D velocities and metallicities consistent with BH 261 reaching to ∼0.°5 from the cluster are identified. A handful of these stars are also consistent with the spatial distribution of potential debris from models focusing on the most recent disruption of the cluster.