'bah' originates from English imitative/onomatopoeic origins, specifically an exclamation imitating a sound of contempt or dismissal (no clear older root).

'bah' appeared in English usage from at least the 18th century in forms such as 'bah' or 'bahh' and has been used as an interjection of contempt since then.

Initially and historically it meant an onomatopoeic sound expressing contempt or disdain; this core meaning has remained largely unchanged.