It is about 490 miles, but would not necessarily be the fastest route due to the quality of roads.
the shortest air route is a great circle
The shortest distance is via Fort Worth and Amarillo using Interstate 45 and US 287, however the fastest route uses Interstate 35 North and Interstate 70 West.
who am I
The route with the shortest driving time is about 360 miles.
Great Circle Route
The shortest route between two points on the surface of a planet, when routes are limited to the planet's surface, is the arc of the great circle that connects the two points. The shortest route between two points anywhere, without regard to intervening matter or energy preventing the route from being followed, is always the line connecting the two points.
Take I-84 EAST to I-80 EAST to CHEYENNE in Utah.Take I-80 EAST to I-25 SOUTH to DENVER at EXIT 359A in Wyoming near Cheyenne.Take I-25 SOUTH to Denver.
If you mean by the words "direct route" the shortest distance between two places, distances between two places are shortest at the equator, because of the shape of the planet. If you mean which direction should be traveled to minimize distance, the route taken should be as straight a line as possible.
straight line
Because that location is the lowest, shortest route between oceans.
This is an approximate travel time . The actual travel time may change depending on traffic,weather conditions and the route chosen. The travel time between the above mentioned places is 23 hours, 11 minutes