Below is the only IB Boarding School located in Mumbai which you are looking for .

Singapore International School
On National Highway No. 8, Post Mira, Dahisar, Mumbai, Maharashtra 401104 ‎
022 2945 2185 ‎

Few other IB Boarding Schools located in Mumbai is given below:
Dr. Pillai Global Academy
Plot No. 1, RSC 48, Gorai-II, Mhada Layout, Borivali West , Mumbai

N.E.S. International School
Malabar Hill Road Mulund West , Mumbai

Ecole Mondiale World School
Gulmohur Cross Road No. 9, JVPD Scheme Juhu , Mumbai

Pranjali World School
Shop #155 - 157 K Marg, Junction of Napean Sea Kemps Corner , Mumbai

SVKM
Irla Mumbai