>>9583011. If you're going so slow that you can 'walk' your dog while on your bike, then you're wasting your time on a bike.
2. In order for your dog, yourself, and others around you to be safe, your dog needs to be on a short leash. That doesn't give you any margin for error and your dog, yourself, or both, could become seriously injured (or dead, in the case of your dog).
Either of the above is more than an adequate reason to separate the two activities. If you're going to ride your bike, leave your canine friend at home, and if you want to 'walk' your dog, then 'walk' with him on your own two feet, your dog will appreciate it more, you'll appreciate it more, and it's safer for everyone, okay?