I wouldnt tell mention the LOR right off the bat. Ask them about shadowing first, shadow them a few times and then let a few days pass before mentioning the LOR. Make sure to send a thank-you note right after the shadowing them.
IMHO, you shouldnt make it seem like your shadowing them just for the LOR, even if that is the case. At least this is what Im planning on doing- I've shadowed a few DOs once each and will again once more before asking them.
Also if you need help finding them, ask the doctors that your shadowing if they know others (they usually do). I found several DOs working in the same building that knew each other.