The "Z" in Spanish is pronounced almost like an S throughout most of Latin America, although many in Spain pronounce it with the "th" sound like in the words "thin" or "thick."
Interesting that bocote is pronounced with the accent on the last syllable, "te." Again, an uneducated guess, but it could be a Taino Indian word since many of their words place an emphasis on the accent at the last syllable, much like many of the other Taino words like "huraCAN" (hurricane).
Incidentally, and totally off-topic (but still on topic with trad archery) is that the Taino word for bow is "baira" and for arrow it's "birigua," according to a Quisqueya Taino elder and traditional archer originally from the Dominican Republic (Quisqueya is the Taino word for the Caribbean island of Hispaniola).
Anyway, if Zircote is a Spanish word, then according to my Puerto Rican Spanish, my guess is that it's pronounced "Zeer koh teh."