Couple of decades ago I spent lots of time on land adjacent to various parts of Shenandoa NP.
Often saw bears BEFORE hunting season, as well as several denning-living areas. ALL bears I saw were eager to depart, once they knew I was there. Don't know if that would be same well inside park. Momma with cubs likely to be a different situation, in any case. These bears were overflow from the park and mostly went back into park during hunting season.
Also now and then saw places where two-legged critters had used these remote areas, inside and outside the park, for extended times and in ways not consistant with ordinary one-two week campers. Never found any active sites.
I was always armed.
Niklas