Let me see if I have this straight. You have music files that you would like to transfer from your computer to your phone? Is that correct?
If it is, you might be able to find a cable you can directly plug your phone into your computer. Many many phones have that today. But, if you are wanting to do it wirelessly with bluetooth, you will need a bluetooth adapter, which sends out the wireless bluetooth signal. You will then most likely need to install the adapter software on your computer, and back when I did it, you'll have to pair your phone to your computer.
Before you go and buy the bluetooth adapter, make sure that you will be able to transfer music files to your phone. Nowadays, more and more phones seem to be locking their bluetooth out from accepting music files through bluetooth. Make sure you can transfer music files through bluetooth first, else you will be wasting your money.
EDIT: A couple of things. 1) You don't need an Internet connection to transfer from computer to phone, and thus, your wireless network really doesn't matter. 2) You shouldn't need your bluetooth headset at all to transfer files.
