One thing I would like to add is that with that personality type, you don’t want to JADE- Justify, Argue, Defend, or Explain. Any reason you give her she will hear as a negotiation, regardless of your intent.
You can say “no,” politely, but keep it as brief as possible and don’t explain. Just say “no thank you,” or “I’ll be riding alone,” if she pushes at all, just keep repeating those same phrases, calmly, and assertively. You can even smile to lighten the blow. But the answer must remain “no”
Most of the time people like her will stop asking if you don’t engage in their drama