If this is your first trip to JA, a few things you should know about the route taxi/bus system.
The vehicles are usually regular size automobiles that sit 3 or 4 passengers in the back seat, and 1 in the front seat (not big buses). They have a set route and do not stop for bathroom or beer breaks. They generally drop you off at the roadside of at the designated bus stop. If you know where you want dropped off on the beach road, let the driver know before you get there. If you are staying on the West End/Cliffs, you can ask the driver if he can take you there for additional price (of at least $100 per person). If he can't take you, you will then have to hire another taxi to get to your hotel.
I agree you would be better off with a private taxi (which will cost between $60 & $80 in total for the four of you (and they will likely have a free cold beverage waiting for you in their vehicle) and you will be in Negril in about 90 minutes from the time you leave the airport. Plus the driver will help you with your luggage.
As you are arriving late in the afternoon, it will likely be dark by the time you get to Lucea if you use a route taxi. Make sure you keep you eye on your luggage so it doesn't disappear or get put into a vehicle that you are not travelling in. As there are 4 of you, you may have to wait for a route taxi that has enough room in the vehicle for all of you and your luggage. Also make sure that it is actually a route taxi with a red plate that you get into - route taxi's have their routes painted on the drivers door and always have a red licence plate (which tells you the vehicle is properly licensed and insured to carry passengers).
Route taxi's are a great way to travel short distances without luggage, but they can be exhausting if you have multiple route changes and luggage for several people.
Have a great stay in Jamaica and enjoy to the max!