How do you know they don't?
First of all, it isn't that they don't like each other. In fact, most vampires don't even know dragons exist. The ones that do know better than to get in their way...usually. Dragons know about vampires and don't like them, but unless a vampire does something to annoy them directly, they don't usually pay them any attention. They are literally beneath their notice. The whole feud between vamps and dragons doesn't get going until the events in the first book.
Suicide bombing probably wouldn't work, depending on the bomb. It would almost certainly kill the vampire, but probably wouldn't kill the dragon. Even in human form, they can take a great deal of punishment. Also, dragons have very acute senses in all forms, and would most certainly smell an explosive-laden vampire sneaking up on them and put two-and-two together.
As for nukes, it's not as easy to get (or build) nuclear weapons as they make it seem in movies. Even if the vamps did get one, what would be the point of killing a dragon with it? Most world governments are aware of vampires, even if they don't make this knowledge public. If vampire terrorists detonated a nuclear weapon for any reason, they'd attract quite a bit of attention. Vamps aren't particularly smart, but they aren't all idiots. This says nothing for what the dragons would do in retaliation. Yeah, they might kill one or two dragons by detonating a hard-found nuclear weapon, but every other dragon on the planet would then declare open season on vampires and start ripping them to pieces. It would not end well for blood-suckers.