Monday, 24th. Travelled about 13 miles today over rolling prairies and arrived at the Big Vermillion, a branch of the Kanzas. Here we were obliged to stop, the water being so high as to render it impossible to cross the waggons.
The river that Bidwell calls the Big Vermillion is the little unlabeled tributary of the Kansas River on this map, located between the dates May 21 and May 27. They are making their way to the Platte River, the highway to the west.
You might be picturing John Bidwell seated on the wagon, driving his oxen, but that was not the way that oxen were driven. They were not guided by reins like horses or mules. The driver walked alongside the lead ox and guided it with a stick. John Bidwell would walk all the way to California.