Bounded-collusion identity-based encryption (BC-IBE) is a variant of identity-based encryption, where an adversary obtains at most d secret user-keys for a collusion-parameter d. From results of existing work, there are generic constructions of BC-IBE, which starts from public key encryption (PKE) schemes with several properties. In particular, we consider BC-IBE schemes constructed from post-quantum PKE schemes submitted to the NIST-PQC competition (denoted by NIST-PQC PKE schemes). Although it is possible to construct a post-quantum BC-IBE scheme by applying a NIST-PQC PKE scheme to an existing generic construction, the public parameter-size of the resulting scheme is not compact. In this paper, we propose a post-quantum BC-IBE scheme whose public parameter-size is more compact. To this end, we construct a new generic construction of the objective BC-IBE by employing probabilistic group testing techniques, while existing BC-IBE schemes are constructed by using error-correcting codes or cover-free families. As a result, we can obtain post-quantum BC-IBE schemes with more compact public parameters by applying NIST-PQC PKE schemes to our generic construction.