In fleeing from gunfire, they had run into the Tardis, not managing to shut the door all the way in their rush. The shields took care of the gunfire, so they didn't notice in the flurry of activity as the Doctor piloted the Tardis into the time stream as fast as he could. As River caught her breath, leaning on the closed door, they hit a bump. Afterwards, the Doctor could not say what that bump was, but it jarred the door open enough for one archaeology student, her Master's degree not quite obtained, to tumble out into the time stream.
It all happened so fast that he only had time to scream her name at the top of his voice, dashing to the door, reaching out as she tumbled outside the Tardis's safely shielded little pocket of air. With only moments, he moved faster than he had ever moved before and likely ever would again, rushing to spin the wheel, pilot it back to her. As she fell back into the Tardis's bubble, he pulled her into his time machine, running his hands over her body, checking that she wasn't missing anything.
She was shaking and her expression conveyed a mixture of terror and overload of information. His hands slowed as he verified that she was in one piece and had not grown any extra limbs. He led her to the chair, sat her down, and had the Tardis scan her. It only took moments in the time stream to dissolve into time forever; it was a miracle that she even came out, let alone undamaged.
She was young; these were early days for them. She still questioned him with genuine curiosity, not with scorn. She still had a radiant innocence about her. Her eyes were enormous and they swallowed her face then, wide from fear and confusion. She bent herself in two, and threw up all over the floor. Immediately afterwards, she dissolved into hysterical tears.
It took hours for her to stop shaking, and hours longer for her to sleep in her room in the Tardis; she was not a full-time companion and had never been for him. Perhaps one day, if future-River's hints weren't all teasing, she would be.
"I want to go home."
It was the first coherent thing she said, and it had taken her two days to say it. He obliged, leaving her in her dorm room. She hadn't lost all the fear in her eyes yet, but she had allowed a hundred and more tests to be run, and after being assured and reassured that she would be fine, she spoke her singular sentence and left him. The next time they met was over a year later, and she waited for him with a laser pistol and a list of questions. They did not speak of the day she had fallen. They merely picked up where they had left off. These days, these middle days, were when things were linear. The next many years of their meetings would be mostly linear, and she even travelled with him for short spans of time. But she was River Song and he was the last of the Time Lords. Nothing with them was ever simple or easily explained.