Accurate prediction of surface pressure distributions is critical for the aerodynamic analysis and design of high-speed axisymmetric bodies, particularly for configurations such as spherically blunted cones and flares. Traditional computational fluid dynamics (CFD) provides reliable results but is computationally expensive, especially when evaluating numerous geometrical variations. To address this challenge, we propose a Bidirectional Long Short-Term Memory (BiLSTM) network as a data-driven surrogate model for predicting the pressure coefficient (Cp) along axisymmetric surfaces. The BiLSTM leverages the sequential nature of surface geometry to learn both local and global flow features from a compact dataset of high-fidelity CFD simulations. Eighty geometries, each defined by seven key parameters, were simulated at Mach 2 using two-dimensional axisymmetric CFD under laminar flow assumptions. Comparative studies with feedforward neural networks (FNN) and unidirectional LSTM architectures demonstrate the superiority of the BiLSTM, achieving R² = 0.985 and a mean absolute error of 0.045. The results show that the bidirectional structure effectively captures forward and backward spatial correlations, yielding smooth and physically consistent Cp predictions, particularly near stagnation and flare compression zones. This framework provides a computationally efficient, high-fidelity, and generalizable approach for aerodynamic prediction, offering significant potential for rapid conceptual design and parametric studies of complex axisymmetric bodies.