I live in the area. It is safe. Obviously, you shouldn't be running late at night alone, regardless. I see lots of 'walkers' and joggers along Tuckerman Lane and Old Georgetown Road which is safer. A lot of traffic runs on Rockville Pike so it's a mixed bag on what Psycho is passing through the city of Rockville (355/Rockville Pike is the main road that runs from the District through Germantown). Crime in the 20852 zip code is very low. I wouldn't run in Rock Creek Park at night alone.
Median income for North Bethesda is above average for Montgomery county and almost double that of the national average.
http://en.wikipedia.org/wiki/North_Bethesda,_Maryland
The area is clean and close to the Metro, Highway, shopping, golf, restaurants. Grovesnor has a nice little grocery store (Corner Market) that is not overpriced. You also have the Giant on Old Georgetown Road - if you need a lot of things. Strathmore hall has movies on the lawn in the summer.
Houses (single family) fun in the high 600-900k and Townhouses run from the Low $600k to $800k.
Tuckerman Station and Tuckerman Heights have nicer amenities amongst the townhouses in the neighborhood since Tuckerman Lane is not as congested as up Rockville Pike (355). There is another nice neighborhood that is on Edson Lane but it is not in walking distance to Grovesnor Metro.
You won't be disappointed with the area.