The background:
Brennan accepted a teaching position overseas & resigned from the Jeffersonian.
Booth worked his way to the AD position at the Hoover.
They parted on good terms with each other and their friends.
They attempt to keep in contact as best they can, however as we all know with long distance relationships life gets in the way.

The snow starting falling softly as Booth left his office on Christmas Eve. He drove carefully and silently to the grocery store on the way to his home. He was batching it tonight, Parker was at his mom's and his own girlfriend had gone to visit her folks in Virginia. Pulling into the parking lot of the grocery store, he parked and headed quickly into the store. Going inside, he went straight to the dairy section to get a gallon of milk, and then decided to see what was available in the heat and eat section, located next to the organic food aisle.
Walking down the aisle he was enveloped in a subtle cloud of sandalwood and cinnamon. Pausing briefly, he smiled. Her perfume. Rounding the corner, he saw a tall, slender brunette silently comparing the two items she held in her hand. Her purse rested slightly on the handle of the cart in front of her. She has a nice figure, he thought to himself, starting to pass to the frozen section, nice boots too. Her phone rang and she answered, "Brennan."
Shocked, he just stood there listening to that honey voice, paralysis broken he hurried over and touched her sleeve. Surprised, she turned around sharply, her bag catching and spilling its contents to the floor. At first they just stood and stared at each briefly and then the recognition dawned.
They reached to hug each other and then bent to pick up her things together, laughing to ease their embarrassment and uncomfortable first glance. Taking their things to the checkout stand they made small talk while they waited for the groceries to be totaled and bagged.
"Why are you here?" He asked as her things were placed into the green reusable bag she'd brought with her. "I'm here to clear up the rest of Max's affairs, and settle the estate."
"I'd heard about that, I'm sorry. Did you get my card?" He asked.
"I did, thank you"
Their conversation was stilted and dragged as he paid for his own things. "Would you like to get a drink?" she asked.
"Sure, Founding Fathers?"
"That would be great" they stowed their things in her car and drove to their old haunt, finding it closed, they tried a couple of others before finding an open liquor store. Booth bought a six pack and they headed back to the grocery store parking lot.
They toasted to the chance meeting and they toasted to the season, both of them were trying to get back to their previous camaraderie from their past. She told them about her architect husband and their life together. Sensing sadness in her voice, he asked her if he made her happy. She smiled sadly and said, "We have a good life, he's a good man."
Booth knew she was a terrible liar and she was being as honest as she could. He told her that he had a girlfriend, but they both knew it wasn't meant to last. "You haven't changed a bit Bones, those blue eyes are just as beautiful as always." Brennan looked at him; her gaze tinged with gratitude, or was it skepticism? "Thank you Booth, you still look as good as always" her voice tinged with regret.
Booth reached for the last beer and said that desk work was boring but safe, although he missed the field. He had a better relationship with Parker though. They toasted to Parker and she asked how he was. Booth told her that he was almost grown and gone, he was joining the Army and asked about her now and then.
They finished their drinks and in the comfort of the car their familiarity and different lives clashed making it difficult to keep the conversation going. Awkwardly, Booth said, "I have to go."
"Yes, I've got to go as well; it was really nice to see you Booth. I missed you more than I knew." She said as she leaned over and kissed his cheek. Pausing too long to kiss her back without being uncomfortable he clasped her hands and got out of her car.
Watching her drive away he was once more back in the lab, watching her walk across the platform, turning to smile at him and melt his soul with the love in her bright blue eyes. The old familiar pain flared up as he turned to go to his own car.
Driving home he realized the snow had turned to rain and the droplets on the windshield mirrored the tears on his face.