I had to deal with the same problem in one of my older fortresses.
Usually I build the bulk of my fortress in the metamorphic layer, deep underground, but I also have an underground farm in the deeper soil layers, an underground greenhouse for above-ground crops, and an above-ground pasture/orchard. This particular fortress had its orchard surrounded with 3 z high wooden walls, with no fancy archer towers or anything. Soon my first goblin siege arrived, and I was calmly watching them pile into my hallway of cage traps when I started getting a load of job cancellation spam and
"Stray Horse has been found dead."
"Stray Alpaca has been found dead."
"Stray Piglet has been found dead."
"Stray Drake has been found dead."
"Stray Yak Bull has been found dead."
"Stray Leopard has been found dead."
and that's when I discovered 2 goblins inside my orchard. I freaked out because I had no army yet, but I waited for a season or so and they eventually climbed out.
I solved the issue by slaughtering all strays and forcing the pet owners to feed their own animals, removing the pasture zone and leaving it as an orchard.
In your case, I would advise building an outcropping of 2 tiles or so wide. You could line the bridge with fortifications, too.