Yes, it was a novel concept the only problem was that darn radiation. In the end the reactor and required shielding weight were substantially higher then was feasible for a bomber.

Because of this shielding was designed as two stage, stronger to protect the crew and weaker around the reactor but that meant the plane was fairly radioactive. If I remember correctly there was also the concern that the use of a direct drive system necessary for weight concerns in place of a two stage systems could spread radiation through the exhaust in certain conditions.

Here is a page on the programs:
http://www.nuclear.com/history/Nuclear_airplanes.html

The soviets had a program as well but considering their safety record on submarines and land based reactors it’s a good thing that didn’t pan out.
http://www.aviation-history.com/articles/nuke-bombers.htm
David