I was under the impression that they had military garrisons, merchants, and maybe even British royalty there. But i've always wondered how long it took to transfer complete control and how long it took to transport British holdings (ships, people, goods)?
Edit: title shouldn't say Bangladesh wasn't in existence yet
I don't know the answer to your question, but when the British left they created two states, not three - India and Pakistan. That state of Pakistan was actually two parts separated by India - what is now Pakistan in the west and what is now Bangladesh in the east.
Bangladesh didn't come into existence until 1971 when it separated from (West) Pakistan.