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Abstract We study the conformal bootstrap for 4-point functions of fermions 〈ψ i ψ j ψ k ψ ℓ 〉 in parity-preserving 3d CFTs, where ψ i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.