Fort Lee to Chelsea is about $35-45 each way, plus tip and tolls. Union City should be in the same range. As others have said, you will have to pre-arrange for a UC car service in both directions. Most days, it shouldn't take more than 20 minutes, but if there's any sort of traffic issues, it could easily take an hour.

If you decide to take a bus, be sure to ask at your client which one. Most run along JFK Boulevard at the top of the palisades, but many industrial companies are along West Side Avenue near the rail road tracks - which would not be walkable. And some stop at every corner along the way, which could make for a very long ride.