I have an eFax account... premium one... but you can get a free one. With a free acct, your (eFax) fax number will have an area code other than your own - but if you're only using for sending, that doesn't matter at all. Once the acct is setup, use your desktop browser to locate and their online send fax page. Send the link to your BB and you'll find it works (despite the fact that eFax support says you can't send faxes from a mobile device). It looks a bit funny on BB browser but does work.
I'm on a apple laptop which has a built in fax program where I just need to plug in a phone line. Since i'm already using my BB curve has a modem to tether... can I use my BB curve as a modem to send fax as well?