Exploding bumper: Oh, so that's how it's supposed to work. I didn't know there were shock-absorbing pistons in modern bumpers. It makes sense on the face of it that a pressurized tube of gas could potentially explode if heated. But as their first test showed, it's not something that just happens as a matter of course.
Not surprised that Adam couldn't start the fire until he went into the, uhh, cockpit? cabin? What do you call the inside of a car? Anyway, in that larger space, the gasoline vapor wouldn't have been as concentrated, so it would've been closer to the right ratio of gas fumes to air.
An interesting set of tests with the piston. It's reassuring that these car parts are designed so well that even the Mythbusters can't make them fail dangerously.

And the guys showed they have a good grasp of physics -- Adam's idea about the bumper as a heat sink, Jamie putting the metal plates on to diffuse the flame.
It's an unusual situation for the Mythbusters: they get direct, firsthand confirmation that this event has happened, so the myth's confirmed, but they can't reproduce it or figure out exactly how it had to happen. That's kind of frustrating.
So of course they faked it out with gunpowder. And they call it busted, which I guess it is on the specifics of the myth as stated, that the bumper could fly 50 feet. But I'd call that just an exaggeration rather than a myth, since it's confirmed that a bumper can explode outward in a car fire, however improbable that may be.
Horseback arrows: Both the myths this week are above average for this season so far. I like it when they do things from history like this, and the physics is interesting. From the first test, it looked like the speed of the horse did increase the arrows' velocity and momentum, so as Kari said, that left the question of how momentum correlates to penetration. It should increase penetration, since force equals mass times acceleration. But by how much?
This seems to have been taped earlier than some of the other myths, since Kari doesn't look pregnant. Actually I thought she did when riding the horse, but back in the shop where she was carving the horse's head (and I'm wondering where the obligatory
Godfather joke was), she was wearing a close-fitting top that showed no sign of pregnancy. And I doubt they would've done the first test a month or two after planning the second, although I suppose it's possible that portions of the testing were staged/recreated for the cameras.
The car/crossbow tests went well and provided some good data. I would've liked to know what the arrows' actual speed was so I could figure out if that 31% increase in velocity was accounted for by the 40 mph of the car (which would mean the arrows' speed from a static start was 129 mph), or if it was less than that and air resistance was diminishing the velocity increase. Anyway, this is the same as the previous myth: the underlying concept is confirmed, but the alleged magnitude of the effect is busted. Firing while in motion does increase the speed and penetration, but not to the extent believed/claimed.