Agreed fax is much safer but once you have a PDF of your return in your possession you can attach it to an email if you want to.
You need your tax returns as PDF files. If you filed using a paid version of turbotax in 2015, both your 2014 and 2015 files should be available to download from your online account. Don't download the tax data file (or you can, but don't send it to the bank as it won't be usable by them--its's good to have anyway.)
If you filed with turbotax installed on your own computer, only you have the PDFs of your tax returns.
Since the PDF tax returns are unsigned, you may hear from the bank that they want a signed copy. In which case you will need to print the returns on paper, sign them in ink, then mail, FedEx or Fax the return to them. If the bank will accept the unsigned PDF, you can attach them to email. They are as secure as you have made your email account (weak or strong password, reused or unique, etc.)