Once you've made your way to Survive Bar, you can start socializing with your party members to deepen your bond with them. This can only be done if their bond level has reached the lock. You get bond points for participating in battles, eating out together, participating in Table Talks, and the other conversational pieces your members may have while out and about.
The max level is 5 for Adachi and his story involves the background reasoning for going after Horinouchi. The choices during the events will increase one stat. He will probably be your first one maxed since you get a level immediately through the story, compared to the others. Any time you end up getting the bar filled, head on back to progress the relationship.
If it does not appear that you can interact with the character, you will probably have to wait until the story progresses further, as in the case with Nanba.