How about loose formations? Covering fire? Basic tactics that have been around since WWI that Caesar rejects because he likes to emulate Rome far beyond what is healthy.
Formations won't help on a small bridge with no Cover.
You just rush across as quickly as you can.
And his ideas of sending in the newest recruits is a good idea.
And Caesar actually use's Artillery to try and weaken the NCR on the far side of the river.