When you imbed a certain kind of nuclear materal [alpha emitter, I think] in beryllium, you get a thermal neutron source.
To imbed an explosive in a dirty bomb of nuclear material and set it off requires a great amount of danger to the bomber as well as a lot of transportation and logistical problems. I tend to think the actual nuclear bomb is a bigger danger than the dirty bomb.
The Iranians, Iraqis, North Koreans, or Pakistanis would be happy to get one delivered over here if the transport problems could be solved and the origin covered up. The origin gives them more pause than the transportation problems.