“Station du métro” relates to a specific “métro”, i.e. a specific metropolitan railway network. Either a specific network must have been mentioned previously or the context must make it clear which network it is.
“Station de métro” relates to “métro” as a concept. It's the same construction as “roue de voiture” (car wheel): when referring to an attribute of a generic concept, the generic concept is introduced by de without an article.
Historically, at first, both were used, but over time, “station de métro” won. If you look at examples of occurrences of “station du métro”, you'll notice that it's often spelled “station du Métro”: Métro is capitalized because it refers to one specific network (usually Paris's network, in French). Over time, as the generic concept of a “metro” lost its novelty, “station de métro” won.
Similarly, a bus stop is “arrêt de bus”. A train station is “gare de chemin de fer”. Note that this is always a reference to the network as a concept, not to a specific vehicle. For the Paris RER, which denotes a specific network, “gare de RER” is more common but “gare du RER” is also used. For taxis, however, both “station de taxi” (referring to the concept) and “station de taxis” (referring to the vehicles) are used.