Garmin used to make a bike mount for this GPS, but doesn't look like it does anymore. It still makes the "Rail Mount Adapter" but it looks like you have to buy one of the other mounting kits to get the appropriate battery cover to use with the "Rail Mount Adapter" to put it on a bike's handlebars. The attachment of the battery cover to the GPS was weaker than the connection from the mount to the battery cover, as I recall.
IIRC, a lot of people have had problems with the older etrex on bikes related to the reliability of the electronics, which might be why Garmin doesn't sell an outright bike mount kit anymore. It has to do with the battery connection springs connection to the circuit board not being designed for this use. They bounce and it cuts power to the receiver. This is another reason why a lot of folks toss their etrex into a pack or pocket.
These is probably big reasons why the new etrexes (and the Oregons and Dakotas) have a new mount system that works a whole lot better.