If Bridge from Below isn't in your graveyard immediately before a creature dies, its abilities won't trigger at all. If Bridge from Below isn't still in your graveyard as its first ability resolves, you won't create a token.

While Bridge from Below is on the battlefield, it has no effect. It does something only if it's in a graveyard. Yes, this is a bit weird.

If a nontoken creature you control and a creature an opponent controls die at the same time, you choose the order in which Bridge from Below's triggered abilities resolve. You can create a token before you exile Bridge from Below.

Neither ability cares who controlled the creature that died, only which graveyard it was put into. This means that if an opponent controls a creature you own, its death causes Bridge from Below's first ability to trigger, not its second.