Based on the posts in this board, I can see that there are trains and buses. I have sampled the trains in London, Hongkong and Japan which are all convenient because of the system employed. Pardon me but I have seen photos in social media that trains and buses are too crowded. Let us know if those pictures are just for effects or are they true that public transportation in India is not convenient. Even us tourists cannot rely on taxi all the time because it is expensive, much more the hotel car. That's why we always take the public transport whenever possible.
What you see in the photos is true, the buses and trains are crowded, but buses are more crowded whereas the national train system is reasonable, as the tickets have to be pre-booked. Local trains, however, are slightly crowded, especially during the office hours. So if you do wish to travel to another destination in India on the national rail then there is no issue with it being crowded as you just have to pre book your ticket in advance to get a confirmed ticket. With the local trains just try to avoid the morning hours and evening hours to avoid the crowd.
A lot has improved since those images I am sure. There is the sea route at Mumbai from Bandra to Worli for example which is less crowded and a pleasant joy ride. The image says it all There air conditioned buses all over India for local travel, which are not crowded. You could get a timetable for these buses and the routes concerned. Agreed trains are crowded at peak hours but tourists could choose off peak hours and travel I class. A bit of planning can make your travel by bus and train a great experience. Welcome to India. Source: Maps of India Bandra-Worli Sea Link.