baby rose vs rosebush

baby rose and rosebush both are nouns.

Word	Noun	Adjective	Verb	Adverb
baby rose	Yes	No	No	No
rosebush	Yes	No	No	No

As nouns, rosebush is a hypernym of baby rose; that is, rosebush is a word with a broader meaning than baby rose:

baby rose: vigorously growing rose having clusters of numerous small flowers; used for hedges and as grafting stock
rosebush: any of many shrubs of the genus Rosa that bear roses

Other hypernyms of baby rose include rose.

baby rose (noun)	rosebush (noun)
vigorously growing rose having clusters of numerous small flowers; used for hedges and as grafting stock	any of many shrubs of the genus Rosa that bear roses