@ijsa I have purchased via the BSES scheme this year as well. The process is pretty straightforward and totally online, atleast for BSES Rajdhani.
Step 1. Login
Here. Username and password will be CA Number.
Step 2. After registration, you can select which Model you want to go for and apply for that.
Step 3. You can check out all the authorized BSES showrooms from where you can buy. Some showroom's do start calling you that they have received a request but you can buy from the showroom which is nearby.
Steps and locations are mentioned
Here as well along with all the required documents. You will also need to show a bill copy.
Here is a link to a PDF shared by bses.
Hitachi is no longer included in BSES replacement scheme and atleast for BSES Rajdhani, you don't have to call anyone. All you have to do is an online registration and then with the necessary documents, you can visit the mentioned showroom.
EDIT : Just checked for BSES Yamuna, the process appears to be the same.
This link can be used to login and then fill the details.