Left hand side.
Trigger Bell is specifically designed to be ergonomic and fit in the tiny space under your handlebar, brake and around any gears and so for the moment is available only for the left hand side. Also, where bikes have gears on just one handlebar (eg some twisties) they're most likely to be the right hand side, so the left is more likely to be totally clear for your Trigger Bell.
That is unless you have trigger shifters on the left hand side. With these gears, as in the note and photo above, Trigger Bell fits above the handlebar and on the right hand side. The reason is that the index finger lever on the left hand side is in the exact position that Trigger Bill would normally fit in. Having Trigger Bell on the right hand side still has its advantages in that it's still easier to ping and closer to your thumb than a traditional bell closer to the stem, so there's less movement needed. However, the trigger is now above the handlebar so you would have to loosen your grip to ping.