When you pot up basil (and lots of other plants, too) you leave half an inch of space between the top of the soil and the rim of the plant.

When you do this it is easier to water the plant well without having water and soil slopping over the sides.

Basil grows pretty fast when it is in a warm place and has enough water. In its new pot there needs to be about an inch of new soil/mix under the plant and about the same between the outside edge of the root ball and the sides of the pot.

You say you have roots showing on the surface: you could put some fresh soil over them but stay clear of its stem. Some plants do have roots which rest on or very close to the surface of the soil. Just a light sprinkle, or even some small (half the size of your littlest fingernail) pebbles which will help to stop the surface becoming water-resistant. Water and air can still get past the pebbles.

It's probably better to not leave any of the root ball above the ground. Just the stem/s and leaves. If there is some of the ball above ground it can dry out quickly and your plant will wilt.