I agree that you should just be honest. And while I understand the desire to provide some form of a palatable, but honest, explanation as to why you don't want to ride with this woman, I also think a simple "no, I can't" will suffice, too. If you really would like to explore a friendship with this woman, then feel free to suggest meeting for coffee or something else as an alternative, but I'll be honest that there are already a couple of red flags with this woman IMO, so be careful with how you proceed.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher