You do not need the email to download your IBPS admit card — it is fetched from the IBPS website.
Open the official IBPS website and click the admit card link for your exam.
Log in with your registration number or roll number and password or date of birth.
If you forgot the registration number, use the ‘Forgot Registration Number’ link on the login page.
It can be retrieved using your name, date of birth and registered mobile number.