I trust the tenant, she is known to me, but I would need to email her my bank routing and account #s as well as the "swift" numbers provided to me by my bank. It is the emailing of this information that concerns me. Is it safer to send the information in two emails? From two different computers? The international visa fees are 3-3/4% through the web site provider and we would like to avoid those charges.
It doesn't matter, no amount of security on your end will improve the inherent security flaws in the banking system (just like being cautious about who hears your social security number doesn't help you in the more likely situation where a bank or government database gets leaked and yours + a million other social security numbers are sold multiple to syndicates worldwide)
Just email the bank account, routing number and SWIFT code.
This is a non-issue. Your bank's routing number and SWIFT code is not private information. Your bank account number and routing number is also written on all your checks.
Your bank routing and account numbers are not secret. Every check you write has them at the bottom of the check. Just e-mail the numbers.
I realize this was asked two years ago, but for anyone else with a similar question, bank transfers within the US use a system called ACH where the bank is identified by a nine-digit number, while international transfers use SWIFT where the bank is identified by a string of letters and digits. Many small US banks don't belong to SWIFT, so you'll have to ask your bank whether they have a SWIFT code. If they don't, they'll have an arrangement with a larger bank to forward SWIFT transfers, but it won't be for free.
You could use asymmetric key encryption (using a tool like PGP or GnuPG) to securely transmit information via email. Essentially, your tenant would generate a private/public key pair, and send you the public key. You would encrypt the information using her public key (such that it can only be decrypted by her private key), and send it to her. Et voila.
A quick google shows a number of guides online for how to accomplish this. Here's one. Good luck!