Ya, you can buy shares listed on the BSE from Zerodha.
If you visit Zerodha Home Page you can read that they have more than 5 lakh clients and they share 5% of daily retail trading volume across NSE, BSE and MCX.
It means you can buy shares listed on NSE (National Stock Exchange), BSE (Bombay Stock Exchange) and also buy contracts on MCX (Multi Commodity Exchange) through Zerodha,
Besides, you can also invest in Mutual Fund on direct mode through Coin platform in Zerodha without paying upfront and trailing commissions.
As you know, Zerodha is the largest discount broker in India for their innovative ideas, advanced trading platforms, brokerage and services.
So, you can visit the account opening page of Zerodha and open Demat and trading accounts instantly: