My husband and I have routinely taken both Myra, Princess of Pout, and now Kiara, Princess of Play, bike riding with us. Instead of having them run along side and risk being pulled off course and down, we have used one of those child carriers attached to one of our bikes. It's not the cheapest solution but it has worked very well for both of our Kerries. We padded the bottom with pillows to make the seat even for them and then strapped them in with the car harness and took off.
Before Myra crossed the Rainbow Bridge, she loved riding out with us and would sit in the carrier and just look around like the Princess that she was.
She would ride as long as we did. Kiara is more interactive, moving about to see what is going on but still very settled into her riding throne.
Her tolerance level for rides is only about 30 minutes or so before she wants to be moving on her own but she does enjoy it.
One of the most interesting and fun parts of it is riding along and having people realize that there is not a cute child in the carrier but a DOG! I remember one small child who screamed to his parents "It's a dog. She has a dog in there!" It always gets smiles and outright laughter. But Myra and now Kiara, being the Princesses that they were/are, just took this a part of the adoration they expect and deserve. I do have a photo that I could send you if you'd like to see this in action. Judi and Kiara, Princess of Play (when is the weekend coming Mom so we can go for another ride?"