What is the best glue for a balsa wood bridge?

Short answer: either aliphatic wood glue (such as Titebond Original) or thin or medium cyanoacrylate (CA, "super glue") works. A tight, clean fit matters more than which one you pick, and your contest's rulebook may allow only one of them.

Wood glue (PVA)

Good for beginners. It gives you time to adjust the pieces, sands easily and is forgiving. It needs to be held or pinned until it sets and it adds a little more weight, because about half of it is water that dries off.

Super glue (CA)

Sets in seconds and wicks into a tight joint, so builders can use very little of it. It is less forgiving: pieces must be positioned right the first time, and a joint with a gap can end up starved of glue.

Which one should I choose?

• First bridge, or still learning to cut accurately: wood glue.
• Experienced builder chasing the lightest bridge: CA, applied sparingly with a pin, is common.
• Rulebook restricts glue: do what it says. Some contests limit the type or the amount.

We haven't found controlled tests of hobby glues on balsa, so nobody can honestly give you a measured winner. What the wood-joint references and coaches agree on is that with a good joint the balsa fails before the glue does. See gluing balsa joints for the details.