The map URL is:
https://www.warzone.com/Map/540-Warsaw-Big

I'm in a 2v2 game and my ally is in trouble, I tried sending him reinforcements through the bridge in the middle.
However, he cannot get them off the bridge.
Does anyone know if this is even possible?
And how should it be done?

Based on what I can see, the 5 bridges are all territories that are too narrow to click on. This means that there is no way of interacting with those armies, and that you should use airlift/gift if you want to send armies from one side to the other.

That seems to be the case, but then I really don't understand this map, because it will very likely end in a draw.

It's a very old map. If i remember correctly, now it is impossible to publish a map with too small teritorries, but unfortunately this map was before the proofing was introduced, and it is like that. I guess you have to live with it as even if it got upgraded by the creator of the map or by Fizzer himself, the games currently being played wouldn't be affected. maybe just vote to end?