The prepositional phrase is "On the bike trail", the preposition is "On", and the object of a preposition is "bike trail"
Explanation:
A prepositional phrase is a group of words that is formed with a preposition, an object and a word or words that modify that object. A preposition is a word that connects nouns pronouns or phrases, and an object of a preposition is noun, noun phrase, or pronoun that follow a preposition, in the sentence "Our walk on the bike trail was refreshing." have a prepositional phrase "on the bike trail", a preposition "On" and an object of preposition "bike trail"
No they aren't proper to use in writing class they are considered slang. It would show your teacher that your not interested in sounding educated and proper. Hope this helps!