Generally, TBS is recommended since the phosphorus within the PBS will interfere with the interaction between phosphorylated proteins and its cognate phosphospecific antibodies.
BSA is used as a carrier protein to dilute antibodies and as a general protein-blocking agent in immunoassays and immunodetection protocols. Also, there is a possibility that antibody may get adsorbed on the surface of the vial making it less available for immunodetection as a result of which one may obtain weak signal. So, BSA is used to prevent surface binding of the antibody and therefore forms an important component of the antibody dilution buffer.
You will have to discard the antibody diluted in PBS as it is likely to give you high background as well as low signal for your target protein. But I would suggest you use this diluted antibody and compare the results with the antibody diluted in (1X TBS, 0.1% Tween-20 with 5% BSA).