The border is about 5 miles from Bude on the Holsworthy road, and being a few miles outside could not put you much further from it.
More likely closer.

Further. I live on the Camelford side of Bude. And I never use that road. If I'm driving out of Cornwall I always use either the A39 northbound (25 minutes at least to the Woolley turning) or the A39 nine miles south to Otterham Station, turn left, left again at Wilsey Down on the A395, a good few miles over Cold Northcott (lovely views across to Bodmin Moor) to Pipers Pool and shortly thereafter to the eastbound A30. 40 minutes before I get into Devon that way. You have a point, though no-one in their right mind knowingly goes to Holsworthy. Thanks for your interest.