Nozzles are basically just a more efficient version of this, since they don't waste as much energy which would escape out the sides (it's instead contributing to internal pressure, which pushes everything out the open end more quickly). Burning rocket fuel expands it rapidly, which is essentially all a bomb does. The downside to a nozzle is that you have to keep the internal pressure low enough that it doesn't rupture. This is far less of a problem with an Orion-style ship.
Think of an explosion. They produce moving walls of compressed air that flings stuff around. Though this is just because it's in air, it's a lot of energy. The same amount of energy is still being released if you blow it up anywhere else. (ignoring bonus 'free' energy from e.g. burning the air itself)
Take the explosion out of air, and you still have a 'shock wave' from the material which made up the bomb, and electrons / photons / whatever else materialized from that much energy being released in a tiny space. And it's all moving very quickly.
When it hits your ship's back-end, it gives it a kick. Obviously far less than the total energy released (whatever % of the sphere of expanding energy which your ship covers), but still something. If the explosion is big enough, or close enough, you are still talking an immense 'kick'. And since you have no relatively-fragile nozzle (just an arbitrarily big, thick wall), the force can be many many times greater than a normal rocket.
So to make it survivable, you probably need a big ship and some kind of impact-absorber to take the shock out of it, and / or lots of small bombs that won't kill everyone due to acceleration. Or just get rid of the squishy humans and crank up the proximity / bomb size to whatever you feel like.