Is there a way to test HID headlight bulbs outside of a car?

Just look at the bulb. If it's swollen or discolored it's burnt out. If the bulb looks good the ballast may have failed. How ya like those bright lights now?!

You cannot test a bulb without removing it. 999 times out of a thousand it's the bulbs fault if it doesn't work.

Xenon arc lamps have no filament people.............

Your reason for wanting an HID bulb tester is totally flawed. 

You would still need to remove the bulb to test it.  So if you’re going to do that then use the tester you already own: swap the bulbs across. You rarely need to do that though because a visual inspection will usually clearly show a blown bulb filament.

HIDs have a fairly predictable burn-out lifespan, so unless you know that one bulb has failed for any other reason such as an impact, then you may as well change both at the same time as the remaining one won’t have much time left.

Also: cheap HID bulbs tend to fail really prematurely. The expensive ones include a few additional expensive additions to the tungsten filament material to make it far less brittle. For HIDs, pure tungsten is the worst choice.

Aside from swapping sides, there's no way to test an HID bulb

Keep it simple.  Replace it.  You still need to take it out to get it tested.

An easy way to test a bulb is swap it to the other side ( assuming it is working of course... )