Well, a rocket traveling at close to the speed of light would be very hard to see at all cause it would go from a moon's distance in one direction to a moon's distance in the other direction in a little over 1 second, and seeing a rocket as far away as the moon would be difficult - but I'm thinking that's not what your asking, so lets pretend that we have a perfectly calibrated telescope that follows the rocket so you can watch and follow the explosion.
Assuming that you could watch the rocket approach, fly past and go boom in the process, then, yes, the blast would be slowed down by time dilation. Similar to watching a clock on a space ship flying past the earth, the clock would move slower than normal.
But the clock/rocket ship is a little bit more complicated than it appears. A ship traveling at, lets say, 99% the speed of light but moving towards us (a ship that flies overhead traveling in a straight line, is virtually traveling straight towards us until it gets very close).
Lets say that 2 clocks are synchronized 10 light seconds apart and the rocket is flying towards us at .9C, the rocket will cover those 10 light seconds in 11.11 seconds, but from the rockets perspective, space will be shortened and time dilation of about 2.3, the trip would appear to take 4.8 seconds. Now, consider what you see from earth watching the rocket. It would take 10 seconds to even see the rocket, cause it takes 10 seconds for light to travel 10 light seconds, but then, you'd see the rocket overhead 1.111 seconds later, so the clock would, from an earth perspective, move forward 4.8 seconds in 1.111 seconds, so it would appear to be moving faster, not slower (We're assuming you could see a clock from 10 light seconds away). Then, as it moves away, you would see it slow down.
As to the long streak of a slow explosion. Kind of, you'd see a slow explosion, releasing photons and exploding matter and neutrons and neutrinos happen much more slowly. The photons would be red or blue shifted depending on the relative velocity. so you would see that, and if the bomb took minutes or hours from your point of view to explode, the energy released would be spread out over that time. The matter and Neutrons would travel at less than the speed of light, so from a ship traveling close to the speed of light, you'd probably not see 1 single atom from the explosion, you'd only see photons bouncing off the atoms. The atoms would move at the combined vector velocity which would, from your point of view, be kind of light a flashlight pointing in the direction of the ship.
It's worth pointing out what what you could actually "see" on a space ship moving past you at near the speed of light is iffy anyway, but in theory, yes, if the ship was traveling fast enough you'd see a time-dilated slowed down explosion.
Edit - I read the answer by Ernie and I think I was wrong about the energy being released being the same. It helps, I think to simplify. Instead of a bomb, and a rocket, lets call it a single uranium atom flying past at 99.9999% of the speed of light and it undergoes fission right overhead.
at 99.9999% of the speed of light time dilation would be 707 times. So it would appear to split 707 times as slowly, but the mass of the Uranium would be 707 times greater than a non moving uranium atom, so the rest mass difference between the Uranium and the parts it splits into would be 707 times as great - so, Ernie is right. You wouldn't see a low energy long lasting explosion because the energy would increase in proportion with the time dilation. As to the rest - observing the particle flight path (mostly in the direction of the ship) and the red/blue shift of the photons, those parts I stand by. (sorry for the wordiness, it's how I write)