You learned the reading for 駿 with the kanji, but 馬 has two possible readings in this word, and you only learned ば. Here's a mnemonic to help you remember め:
This fast horse is so fast that all you can see as it speeds past are the whites of its 目 (め).
Of the two readings, しゅんめ is the more common.
The king showed up riding his prized fast horse.
The daimyo was presented with a number of fine horses.
She made a successful bid of 100 million yen for a fine horse with a very good coat.