The square Bi layers in $A$MnBi$_2$ ($A =$ Sr, Ca) host Dirac fermions which coexist with antiferromagnetic order on the Mn sublattice below $T_mathrm{N} = 290,$K (Sr) and $270,$K (Ca). We have measured the spin-wave dispersion in these materials by triple-axis neutron spectroscopy. The spectra show pronounced spin gaps of 10.2(2)$,$meV (Sr) and 8.3(8)$,$meV (Ca) and extend to a maximum energy transfer of 61 - 63$,$meV. The observed spectra can be accurately reproduced by linear spin-wave theory from an Heisenberg effective spin Hamiltonian. Detailed global fits of the full magnon dispersion are used to determine the in-plane and inter-layer exchange parameters as well as on the magnetocrystalline anisotropy constant. To within experimental error we find no evidence that the magnetic dynamics are influenced by the Dirac fermions.