My hypothesis for why Spirit's chase music has bells
Based on the whooshing air in her chase music and the phasing sound effects, the wind is a major part of the Spirit's lore, just like many ghosts and spirits in mythologies around the world. It's an invisible force that can still move things, just like the Spirit.
She also has an add-on called furin, a type of Japanese wind chime. When there are many hung up in a windy area, they ring just like in the Spirit's chase music. I'm guessing that the constantly ringing bells are supposed to sound like a bunch of furin with wind whooshing through them, which you can also hear in the terror radius ambience.
The one sticking point is that furins are made out of glass, and the bells in the chase music sound a lot more like full-on metal chimes. There's probably more types of Japanese wind chimes than just furins but that's the only one I can think of for now, so that's a big problem. It could have also been that furins were too soft to hear, so the chimes are only there to mimic the pattern of ringing furins.