There are three ways you can save a route.
If you scroll down to the bottom of the results, you will find a “Save Route” button.
If you tap on the info box at the top of the results, it will bring up a menu with an option to save the route.
And from the Routes tab, if you drag from left to right on a recent route, it will reveal a Save button.
Conversely, if you drag from right to left on a recent route, it will reveal a Delete button to remove that route from your recent routes.