Compactness conditions as well as estimates for singular values of the bordered Airy transform fAg in L₂(ℝ) are studied for suitable functions f(x), g(x), x ∈ ℝ. Sufficient conditions for the operator fAg to be in the Schatten-von Neumann class S_p, p ∈ (0, 2), are obtained. In particular, certain conditions ensuring that the operator fAg is in trace class are given.