Next from English Grammar Today "is an adjective, an adverb or a pronoun" As a pronoun, it can be used with or without 'the'. In Oxford Dictionaries it is called a ‘noun’ and use of the article is frequent. Is the sentence 'Our bus stop is after the next' correct with the article or without?
Next belongs to three word categories: adjective, adverb and preposition.
The next train leaves at 13.45. [adjective as modifier of “train"]
The play was next performed in 1901. [adverb as adjunct of serial order]
Ed sat next to the mayor at dinner. [preposition as head of PP]
In your example Our bus stop is after the next, the adjective "next" is a fused modifier-head interpreted as “next bus stop” (or "next one"), in which it is simultaneously head of the NP and modifier of "bus stop" (or of the noun "one").
The bigger fish usually eats the smaller.
The fastest usually wins the race.
The meek shall inherit the earth.
Superlative adjective fastest and comparative adjective smaller and the base meek are nominalized there.
The same thing can happen with next (which is actually a "collapsed" superlative meaning "nearest").
The next to open his mouth gets detention.
It can be nearest is the locative sense or nearest in the sense of temporal sequence.