Depending on the vehicle, a base plate installation can take anywhere from 2 hours to 8 hours. Most times, you can expect about 4 to 6 hours of labor, if its a typical installation where they have to remove front fascia plate, drill holes, mount the plate, then put it all back together. It is not difficult work, but it is time consuming, having to take all that stuff apart, mount the plate, and put it all back together. That's why labor is what it is.
Definitely shop around, though, as some places want to charge for the exact, actual time their tech will work on your car. Others will just give you a flat # of hours and charge that regardless how many hours it really takes. I've had base plates installed that took the technician all day, and only got charged for 5 hours of labor. The other extreme can happen, too.
One time I had a base plate installed by the Ford dealer. Had just bought the car brand new there a few days before, figured they'd know the front end of it really well and would do a good job since they knew me well and I had bought the car there. They did, too, and only charged me for 3.5 hours of labor.
I just had one done (base plate) on the Ford Taurus about a month ago. Talked to 3 different RV places, ended up going with the Camping Word in Valdosta, GA. Very glad I did. Great bunch there, they did a great job, did exactly what I asked for (including some specific, custom wiring I needed for tail lights and an indicator light). They were very reasonable with the rate, hours, too, for all they did. Highly, highly recommend those guys if you're ever in Valdosta, GA, and need any RV related work done.