Which eTrex? The Garmin eTrex line is quite varied. I own two. The prices naturally vary quite a bit also. They have bike mounts for them but they aren't cheap at around $30 - $35. I didn't like paying that much for a little piece of plastic but the design is really specific for the eTrex. Mine works fine on my bicycle but I have a little trouble reading as I ride. My eyesight is probably a factor. I like using a mapping software like DeLorme Street Atlas to download the track to my computer when I get home. The best part is that you can take it off your bike and use it for hiking, geocaching, etc. I have a Garmin Forerunner 305 that is designed for running and bicycling but isn't the greatest for hiking.
So, the eTrex will work but to give you a better idea of if the price is right find out which eTrex it is (basic (yellow), Vista, Vista HCx (color), Venture, Summit) and then look on ebay. That should give you a general idea.