The BSE is a national stock exchange - meaning it is common to all residents of the country. (Note: There is a separate exchange called the National Stock Exchange. The term national is used to stress on the fact that, the exchange is available nation wide)
A Regional stock exchange is usually located in a particular city and is open for trading only to the residents of that particular city/state which makes it inaccessible for other investors who do not reside in that region.