For battlegrounds, you would want to look at the entire battlegroup.
And find one where the ratio of opposite faction players to your faction is as high as possible in their favor.
Of course battlegroups are a lot of servers.
Maybe you are only interested in the number of level 80's as well.

A BG doesn't start, as in give each player the option to click "enter".
Until both sides have the maximum number of players in the queue.
So, with fewer players queueing on your faction, and more on the opposite, you should get in as soon as enough toons for your side (AB = 15, WSG = 10, AV = 40) are in the queue.
The opposite side, with many more toons will wait longer, because there are fewer members of your faction to go in with.

Imagine a 1 on 1 battleground.
One faction has 4 players queueing.
The other faction has 5 players queueing.
The side with 4, has virtually instant queues.
The side with 5, will occasionally have to wait.
For shorter queues, you want to be on the side with 4, not the side with 5.