Dive India is originally based out of the Andamans with bases at Neil and Havelock. However, they also have training centers in Mumbai where you can try diving out with an introductory course in confined water with instructors. The PADI Discover Scuba Diving starts at INR 4,500 + tax and you'll learn basic theory, skills and diving. They also offer a PADI OPen Water Pool Training course at INR 10,500 + tax that will get you diving ready in 2 days.
Training is offered at the Fr Agnel Swimming Pool in Vashi, Navi Mumbai. Classes need to be booked ahead and medical details need to be shared prior to any training.