If I board the bus or walk into my office building sans velo, I am inevitably asked, "Where's your bike?"
My response, a white lie, usually is, "In the shop." I've learned this stems follow-up questions. Drivers understand having a car in the shop; they can identify with that, and usually just nod and go, "Mmmm." If I say, "At home," or, "Felt like resting today," or, "I'm running home," it just draws more questions. (Number two response to "In the shop," after the nod/hum: "Flat tire?")