What is the best participle and modifier in this sentence. One day my friend, excited about her new bicycle, called me on the phone

Participles have two forms - they either look like verbsing, or like past form of a verb (adding - ed to regular verbs, or third column of irregular verbs). They often function as either adjectives or adverbs in a sentence. So, having that in mind, the only participle in this sentence is the word excited, and it modifies the noun friend. The friend was excited, which is why the latter word modifies the former.