Don't want to travel without Piper anymore but I still have one companion quest to go, Curie's. Is there some fast way to gain her approval? Does it only work with likes, or also time spent while travelling together?

Do Minutemen radiant quests.

From the wikia:

Curie likes when the player character acts selflessly.
Curie likes when the player character is supportive of others.
Curie likes when the player character tries to resolve things peacefully in dialogue.
Curie likes when the player character protects the USS Constitution (and the robot crew) from scavengers.
Curie likes when the player character completes missions for the Railroad.
Curie likes when the player character joins the Brotherhood of Steel.
Curie likes when the player character uses her aid to save Danny Sullivan.
Curie likes when the player character talks to Miss Edna in the Diamond city School about love.
Curie likes when the player character explains to Moe Cronin in Diamond City that baseball was America's favourite pastime and not a violent bloodsport.
Curie loves when the player character completes the experiment at the Cambridge polymer labs. However, if the player completes the experiment after overriding the defense systems, Curie will not react.
Curie loves when the player character defends synths when meeting Desdemona.
Curie loves when the player character brings the experimental serum to Virgil.
Curie loves when the player character argues about the importance of friends with Sinjin.

Pretty much covers all "good" companions.

Thanks, I guess I'll go with the boring radiant Minutemen quests. I much prefer doing the unique quests while travelling with Piper.

Which happens to be most of them haha

@Gelmer you asked for a quick way, and that's probably the quickest.

The USS Constitution quests are kind of annoying but Curie loves you for it when you finish. (Hint: use the lifeboat at the back of the ship for easier on-off).