The Hiroshima bomb, which was a uranium gun bomb, was quite easy to set off accidentally. It was just a gun tube, with a propellant charge of powder in a silk bag, just like naval guns of the period, and fired by an ordinary detonator. The crew of the Enola Gay was under orders that if they had to return to base, they were to drop the bomb into deep water, rather than trying to land with it. It could easily have been set off in a crash or fire.

The plutonium bomb was an implosion bomb, and had to be set off with the simultaneous (< 1us difference) firing of all the explosive lenses to get a symmetrical compression. This was done by charging up a big capacitor bank and discharging it through a krytron switch (like a thyatron or SCR; there's a turn-on gate, but no turn-off) into resistance wires used as detonators. There were no intermediate explosive detonators; they weren't consistent enough on timing. Any inconsistency on timing would cause the explosion to blow out on one side rather than achieving full compression. That still might produce a "fizzle yield", tons rather than kilotons of TNT.

"Single point detonation safe" bombs came years later.