Can I purchase a game bundle as a gift even though I have already purchased it?

This appears to be incorrect. I have the Just Cause 3 XXL bundle and the "add to cart" button is grayed out and inactive. There appears to be no workaround but I could still purchase everything as an individual item and forego the bundle savings.

You can buy an app (game or software) as a gift whether or not you own it. You can also buy a sub (bundle) as a gift even if you have none, some, or all of the apps in it.

Just add it to your cart...

Then select Purchase as a gift

Then select the method you wish to send or store your gift, either Email my gift, Send my gift directly through Steam, or Store the gift in my inventory to send later

Then just check out and you'll have bought a gift copy of a bundle you already have the games for. That's why it's called a gift. Note that you can not separate the games contained in the bundle to gift them to different users, or use part of the bundle yourself. Bundles are (nearly) always all-or-nothing.