You have a couple options options. The dog-backpack carrier used in conjunction with a harness sounds like the best solution for you & her. A good one will have a loop/restraint that can snap to your dog's harness. It's a pain to get her loaded and on your back without help, but it's probably more secure than strapping her to the bike.



Take a look at Beastriders.com. They make high-end, heavy-duty stuff for getting dogs on motorcycles. Even if their stuff doesn't work for you, you can still get some ideas.
I stitched a tall-walled cat bed to an old magnetic pad from a used-up motorcycle tank bag, and my dog has ridden more than 70,000 miles with me, (around-town miles, seldom on the freeway).


And of course your dog is a perfect excuse to get yourself a new bike. (It's not really selfish if you're doing it for the sake of your dog, right?) I got my dog a Globe Live 3 last year and I love it. (I mean she loves it, heh heh.)


And the bed was purely an accidental color-match, but it looks like OEM equipment for the bike.