You can do that if you want to risk emailing a tax return--which is not a good idea. But you cannot do that from within the TurboTax software. You can save your pdf and do what you want to with it. Better idea would be to print it and mail it to the bank certified mail, or hand deliver it yourself--assuming it is a local bank.
For security purposes it would be safer to either fax the tax return or to hand deliver the tax return to the bank.
The PDF of your tax return can be sent as an attachment on an email if your account allows for the size of the attachment.
To access your current or prior year online tax returns sign onto the TurboTax website with the User ID you used to create the account - https://myturbotax.intuit.com/
Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show. Click on the Year and Click on Download/print return (PDF)
If you used the desktop CD/Download editions installed on your computer, the only copy of your tax data file and any PDF's will be on the computer where the return was created. TurboTax does not store online any returns completed using the desktop editions.