A journey intended to be enjoyed, especially if accompanied, is called a road trip.
While not a single word, the driver could say she was looking for a road buddy or a trip buddy. Buddy can mean
a person who does some activity with you
It has lost its exclusively male connotation and is often used, regardless of the gender of the fellow-traveler.
SUPPLEMENT:
Most abject apologies! I did not make clear that both of the suggested phrases are NOT standard terms or idioms, but merely suggested constructions based on the request. Also, road trip itself is a somewhat slang idiom.