I've actually had market and tailor sessions close on me because a pedestrian pushed my character out of range of the contact.
I say have the character rooted in place during those sessions, and automatically use nonverbal gestures to encourage pedestrians to move around them. Nonverbal so your own character doesn't annoy you while conducting his business.
- Heroes would wave the person around him.
- Vigilantes would give the person a warning glance.
- Rogues would draw his weapon(s) and/or conjure a sheath of whatever energy his powers are based on while glaring menacingly at the person.
- Villains would simply give the person a death glare.