How much is the road going to be torn up? I've had to ride through some contruction zones and always found the flag men (I know there are women too, but 98% of the time it's still men) to be very accomodating to cyclists (we have our own hard hats after all) they usually waved me through a little earlier than the rest of the cars because a bike doesn't need the full lane. You just have to take it a little slower to keep your eyes on all the equipment. If you go this route during commute hours, there's also a good chance they'll have not yet started or be shut down for the day.