I'm no expert in bulldog history, but my guess is that whoever made the first board editor put the light square on a1 without realizing it, and no one corrected them. So it just became a part of the game.
Should a1 be a black square or a white square?

I made the a1 square white, so that the white queen sits on a white square. (same as normal chess).
In normal chess, I've always remembered the rule "queen sits on her own color". (white queen on white, black queen on black).
But when playing with the witch, Black's king and queen are switched, so the black queen sits on a white square (messing up the rule again)!
For versions of bulldog with mirror-symmetry, the rule holds "queen sits on her own color" such as this game I just started adding two popes to the game (check here if interested).
(sorry - we recycled the icon for the dwarf to represent the pope).
To be honest, I don't think it matters much (unless anyone can think of a reason).

The bishops are on the "right" colours compared to regular chess, too. I prefer a white a1, and certainly favour consistency.

The bishops are on the "right" colours compared to regular chess, too. I prefer a white a1, and certainly favour consistency.
I agree

What about a compromise? ...
Lol.😄 Btw, the musketeer board painter defaults with a1 as dark (when setting up a 10x8 board), but customizing the colors is possible. I sometimes switch it so a1 is light, but other times I forget. Nobody has ever left a comment. In one game (due to problems) I switched in the middle and nobody noticed.
In all standard Bulldog chess games - as far as I can remember that I have checked them - a1 is a white square. But in FIDE chess on an 8x8 board, a1 is a dark square. In variants like Embassy chess, Capablanca chess and Grand chess, a1 is also a black square.
So how did our a1 square become a light square?