The reason why this isn't supported, is exactly the same as why you cannot send an .exe attached to an email. This is to prevent people from sending malicious software to phones that are not protected. That is why most Android phones will not allow sending APK's over Bluetooth.
If you still want to send APKs over Bluetooth, it is best to hide the extension (APK) from the application and phone (eg. by zipping or changing the extension). That way you can trick the phone in still accepting the application. You have to then unzip or rename the package to retrieve the APK.
Another way, as mentioned by other people already, is to use an 3rd party application (like AirDroid). This will allow you to transfer the APK.
If you want to install the application, you have to be sure to have "Install apps from unknown sources" enabled. Because if you don't enable this, only apps from Google Play will be accepted.