Solo trip to the smoky mountains as a woman

Hi everyone!

I’m planning a solo road trip soon (27F) with my dog and one of the stops are the smoky mountains. I plan on hiking one of the two (or both) dog friendly trails (gatlinburg and oconaluftee) and driving through the rest. I’ll also be staying in sevierville

My questions are
-is this safe for me to do ?
- is there a likely chance of bear encounters on either trail mentioned ?
- any experiences from other solo female travelers to this area
- any tips / reccomendations?

Every bit of knowledge is greatly appreciated! I’m from south Florida and have never been to the smoky mountains or Tennessee in general