Definitely. I haven't asked her about the bike rack, but I'm definitely considering biking in and driving home with her, and then driving in and biking home, just leaving the bike at the office overnight. But I do feel bad that I'd be making her do most of the driving in that case. It really just benefits me and she loses the carpool lane when I jump on the bike. We will see. I'm going to feel it out over the next few weeks and see how it goes.
You don't have any real onus to ride with her all the time. It's something that could benefit you mutually, but when I did a rideshare there were many times when I or my ride would have to cancel and then it's up to the other person to make their own plans. In those days I actually had to take a bus and then cheap taxi or walk the rest of the distance to work. In fact you don't actually HAVE TO do the rideshare at all if you have your heart set on bicycling. Maybe tell her you've wanted to try it out for your health and give it a go for a little while. I haven't looked back since I began biking in.
