I think that woman overreacted, and was rude.
I ride a bike with Tatiana. I use a front-carrying, pet carrier pouch. It's like a backpack, but it hangs on my front. It has a drawstring top (and an inner leash), and Tatiana sticks her head out. She really enjoys bike rides. I like that she's on my front, so I can clearly see her. Sometimes, I rest one hand on her, and steer with the other hand.
Oftentimes, we get pointed at, and smiles from other people, especially kids.