My opinion- she's recording music, so it's a reference to taking a metaphoric spin or ride on the tape of her reel-to-reel tape recorder.
Edit- probably should correct/expand- I think the reel-to-reel where she is, because that's her world. others might only be in their office typing about the world, so they're riding the carbon ribbon of their typewriters to record & express their view of things.
In general, a line (white lines on the highway, tape on reel to reel, black ribbon tape on typewriter and those lines or boundaries suggested as the parameters or lack thereof of relationships, social norms, etc) is a common theme throughout the whole song.