Bosch was in line to make his T20I debut in the five-match series that starts in Mount Maunganui on 15 March.
Mulder has featured in 11 T20Is but is not a regular at international level in the shortest format with the Proteas sending a much changed line-up to New Zealand that did duty in T20 World Cup.
Only Keshav Maharaj, George Linde and Jason Smith were selected in the 15-man squad from the global tournament, where the Proteas lost in the semifinal against the Kiwis.
The Proteas men's T20Is will all act as double-headers as the matches will follow the women's T20Is on the same grounds earlier in the day.
Proteas T20I squad: Keshav Maharaj (captain), Ottneil Baartman, Wiaan Mulder, Gerald Coetzee, Tony de Zorzi, Connor Esterhuizen, Dian Forrester, Jordan Hermann, Rubin Hermann, George Linde, Nqobani Mokoena, Andile Simelane, Lutho Sipamla, Prenelan Subrayen, and Jason Smith