Usually these past autonomous forms end in the “ú” phoneme, but that would be weird here because the vowel here is part of the verb stem. Do you just say “bá”, or is it like “báú” (which would be weird, I think)? (In Munster, it would be like “bách” I assume).
bádh is just a spelling form. There is no further written vowel because “báadh” or “bá-adh” looks odd.
But whether you use the old spelling báidheadh or the new one bádh – it is the same word /ba:u:/ in C and U or /ba:x/ in M.
It is the same suffix /u:/ in C and U or /(É™)x/ in M (old spelling -adh, modern spelling -(a)dh)
and the same stem /ba:/ (old spelling báidh, modern spelling bá(igh)