The wheel represents death and rebirth. If an object "with wheels" crosses the barrier, it could be perhaps interpreted as an object transcending the cycle of eternity.
The bike helped Keine transcend Mokuo's sense of eternity. Mokou began to notice cycles again, of seasons, of change, of bicycles. Even after Keine is gone, Mokuo would surely remember her.
Keine was always afraid of one day leaving Mokuo behind. Ran's whole lesson about time dug up her fears. Perhaps she wanted a way to slow down metaphorically and physically. Although she knows nothing can go faster than light, she still wanted to go fast enough. To make more cycles and go greater distances. The wheels are Keine's mortality, which she has, upon the end of the story, taken control of. She wants to go faster and faster to make her time with Mokou more worthwhile and memorable.
But take my explanation with a grain of salt, if you choose to take me seriously at all.