Just curious if there's actually any way to handle suicide bombers or are you just supposed to die or lose party members with no way to prevent it randomly? That seems like an odd design choice.

You can run like hell from them :) or snipe them from afar to stop from getting to you. Ideally, they won't even have time to activate the bomb so you can pick it up (caution advised: for safety measures wait five minutes or so and save into different slot after pickup).
The hard part is to spot them watch for "unarmed" and unarmored enemies. And, I believe, they mumble something along the "now the only thing to do is to wait" lines after they activate the device. Pay attention. :)

Indeed, the situation that's happened to me on several occasions is that I get in a random encounter, a suicide-bomber spawns 5 tiles from my clustered party, runs up, activates the bomb and then it explodes before I can get my party members to get away from it.

This happens literally before my party members' first turn in combat. It's that bad.

Happened at least twice.