No, there is no way to search on Rover for a sitter by name. So you haven't overlooked anything.
A few ways to go:
1) email or text her and ask for a link
2) use the map function to zoom in on the specific area she lives in and be sure to check the box about redoing the results for the map change
3) search on Google, using her first name, last name initial, city, and Rover
4) call Rover at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team]
5) if you've used her before, then you can go to an old booking in your Inbox and start from there.