Ba- or baa- is an Urdu prefix which means with. For example, you might have heard the word ba-izzat (especially if you have seen those movies of '70s where 'dafa 302' was an essential), which means with honor.
Anyway, bakhuda has ba prefixed to khuda, ie God. Hence bakhuda means, with God, or in god's presence, which is simply known as 'by God.'