Wireless communication speed depends on many factors, not just distance, but also what's between the two things. A car is generally not a great thing to try to send signals through; a messenger bag on a bike is not much more difficult than air.
Streetpass also transmits a variable amount of data. If you have no games aside from Streetpass Plaza, it will finish faster than if you have to transmit information about several games. (I don't know if Streetpass can do a "partial" transmit - sending and updating each game individually.)
In ideal circumstances, 10 seconds is more than enough time. I have seen a Streetpass happen 2-3 seconds after closing my 3DS, if my wife's 3DS is also suspended and in the same room.