This study retrieved novel abundant exact solutions for the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation using the improved generalized Riccati equation mapping technique. The B-type Kadomtsev–Petviashvili equation is of high importance in modeling nonlinear wave propagation in weakly dispersive media in fluid dynamics and plasmas. The derived solutions included singular, bright, and bright-dark solitons, as well as hyperbolic, rational, exponential, and singular periodic solutions. The validation of the derived solutions was confirmed by direct substitution into the B-type Kadomtsev–Petviashvili equation under study. A detailed stability analysis was performed utilizing the linear stability analysis concept. The obtained stability results indicated the presence of neutral stability and the non-existence of modulation instability for any choice of the system parameters. The wave dynamics of some derived exact solutions are illustrated by two-dimensional, three-dimensional, and density plot graphics. Additionally, the results of stability analysis are illustrated by two-dimensional and three-dimensional graphics.