What is the key signature of a major in the bass clef?

Any scale will have the same key signature in both the bass and treble clef. For A major, the key signature consists of F#, C#, and G#.

To write the key signature:

Treble Clef: the sharps correspond to the 1st and 3rd spaces, and the second line [F#, C#, and G#, respectively].

Bass Clef: the sharps correspond to the 2nd and 4th spaces, and the 4th line [C#, G#, and F#, respectively).