Is it permissible to deposit a sum of money in an interest-based bank to obtain a bank statement for travel purposes, and then withdraw it completely and close the account afterwards?

There is no harm in opening an account in a non-Islamic bank for travel necessity, if an Islamic bank is not available, or if the entity only accepts an account from usurious banks. A current account is sufficient if it meets the need, and the funds should be withdrawn from it when the necessity ceases.