In theory, this shouldn’t be that hard. As suggested, just give your bank the exact information you’ve been given. Unfortunately, it’s still not guaranteed. We rented a place in Martinique that required a wire transfer a few years ago. We printed off the instructions and gave them to our bank. It still didn’t go through. We trusted the owner and they (luckily) trusted us, so we just paid everything on arrival. Everything was fine, but it wasn’t without worry.
I still don’t know what went wrong, but do all you can to put the responsibility with your bank. You’re likely going to get charged a fee for the transfer, so hopefully they don’t charge you if it doesn’t work. Of course, ideally it will be pain free.