The question cannot be answered without providing additional information.
There are parts of the Earth's crust which are constantly being eroded away, parts that are undergoing subduction, and so on. Water, wind, flora and fauna can all affect how quickly the radioisotopes are spread from the site.
The size and type of bomb must also be known. Different kinds of bombs produce different radioactive products.
Also, "thousands of years" is not a very precise way to express time.
All in all, I'd say that, in some cases, the evidence would remain detectable for thousands of years, but in other cases, it wouldn't.
- Warren