We study bouncing cosmological models in the framework of f(Q, B) gravity with the functional form \(f(Q,B)=Q+\alpha _1 Q^2+\beta _1 B^2\) . The motivation of this work is to provide a nonsingular alternative to the standard Big Bang scenario and to understand the role of modified gravity in resolving the initial singularity problem. Five representative bouncing models are considered—symmetric, super, oscillatory, matter and Type-IV—and their background evolution is analyzed in detail. The scale factor, Hubble parameter, deceleration parameter, energy density, pressure and equation-of-state parameter are examined, together with the associated energy conditions. Our results reveal that while the NEC and SEC are generally violated around the bounce, the DEC remains satisfied, ensuring causal consistency of the fluid description. Each bounce type exhibits distinctive dynamical features: smooth and symmetric evolution in the symmetric and matter bounces, strong divergences in the superbounce, cyclic behavior in the oscillatory case, and higher-order singularities in the Type-IV model. These findings highlight the versatility of f(Q, B) gravity in accommodating a broad class of bouncing scenarios, which offer a theoretically consistent route to nonsingular early-Universe cosmology.
