We report a high-resolution photoelectron imaging study of cryogenically cooled BiB2- and BiB3- clusters. Vibrational features are completely resolved for the ground-state detachment transitions, providing critical information about the structures of the anionic clusters and their corresponding neutrals. The electron affinities of BiB2 and BiB3 are accurately measured to be 2.174(1) and 2.121(1) eV, respectively. The B-B and Bi-B stretching frequencies are measured to be 1262 and 476 cm-1, respectively, in the ground state of BiB2. Three vibrational frequencies are measured for the ground state of BiB3: 1194 cm-1 (B-B stretching), 782 cm-1 (B-B stretching), and 339 cm-1 (Bi-B stretching). Both BiB2- and BiB3- and their neutral ground states are found to have planar C2v structures in which the Bi atom bridges two B atoms. BiB2- is found to have a triplet spin state (3B2), consistent with its complicated photoelectron spectra, whereas BiB3- is a doublet (2B1) and neutral BiB3 is closed shell (1A1). Both BiB2 and BiB3 consist of peripheral localized Bi-B and B-B σ bonds and delocalized π and σ bonds.