Some more detailed information from someone who actually did it within the last several months on buying tickets in Kolkata for Maitree (Dhaka) and Bandhan (Jessore/Khulna) Express.
Tickets are available at ER Fairley Place Office at the International Counter in addition to Kolkata International Station's International Counter. Fairley Place opens at 9am and is open till 5pm. Kolkata International is open till 9pm.
Ticket can be purchased by either the traveler or a designated agent, but the traveler's Passport and Visa must be presented at the ticket counter. No copies of any sort accepted. So naturally no tickets using any method that makes it impossible to present the original documents. So no internet.
It is recommended that one gets to the Ticket Office before 9:30 am to get the ticket application form. Tickets are sold in order based on the number on the form. The earlier one gets in the earlier and more likely that one gets ticket. Lines can be long. Fortunately on can get a Return (round trip) Ticket.
The procedure is same in Dhaka. Tickets are available from Dhaka Cantonment station. Similar procedure for buying tickets at Jessore Station and Khulna Station for Bandhan Express.
Security is much tighter on Maitree Express than on Bandhan Express. Apparently a lot of smuggling from India to Bangladesh happens via Bandhan Express mostly in Chair Car. So on that train it is better to avoid Chair Car.
Here is a recent video of a ride on the Bandhan Express to Khulna, goods smuggling and all, though unfortunately in Bengali, but one may still see it with audio turned down..
Thank you very much jis, kind of you.
I have a question which I assume you wont have the answer to as it probably doesn't apply to you.
Whenever I apply for an entry visa they are often online and arrive in PDF form to be self printed. Assuming I apply say a month before travel then is it typical to collect the visa from a Consulate?
Oh yes, we are talking about a visa for Bangladesh aren't we, not India?