The best value we have for bottom pressure anomaly is SSH - Steric SSH. This includes the contribution to bottom pressure anomaly from atmospheric pressure anomaly.
I'm not sure why you want to remove the effect of atmospheric pressure, but its effect on SSH is approximately an inverse barometer:
η_ib = - P_atm / (rho_0 * g)
Make sure you have the units right, the above are for height (m) not pressure.
I don't know how well it would work, but you could use the tidal analysis to subtract the tides from SSH - Steric SSH since the majority of what is left at large scales is atmospheric pressure effects. See
Tidal Analysis of ESPC-D-V02
Alan.