I see plenty of people bringing bike into stores around here. I wouldn't hesitate to bring my bike in but would make sure it is left in an out of the way place or I'd wheel it with me. If asked to take it outside, I would. Don't know about other parts of the country but it is becoming more and more common for people to brings dogs into stores around here (even grocery stores) without comment from staff so would be surprised if a bike would be an issue.