One - Big Bend has only 118 miles of border and it's not solid mountains.
Two - How the heck is a river a problem? Most of the land beside the river is flat desert or flat grasslands.
A fence would work in some areas, but you know darn well it would be prohibitively expensive and downright dumb to fence much of that forbidding terrain.
As for the river, if this drought doesn’t break soon, they’ll be walking across on dry ground. Still gotta scale cliffs, though.