Taxi on the island are not regulated. They also tend to be expensive.
I believe the most economical way to do this is to contact several of the beach clubs who offered transport included in their day pass price. The day pass would include the amenities of whatever resort you choose loungers, umbrellas, pool, showers some of them have lockers. Have a look at the Beach, Bananarama and Paradise Beach websites, all of these Resorts offer transport included. Infinity may also except they're the most expensive day pass on the beach, they also limit their day passes.
With 6 people, you will need 2 taxis or a van. And you'll need to negotiate. Usually, it's $20 round trip per person if you have more than 3 people to West End by taxi. West Bay is further away, so it would be more. Have no idea how much a van would be.
It would be easier and cheaper to have a transport+day pass package.
Here's another site for shore excursions, but I would personally just book directly with Bananarama.
Thank you !
I am booking through bananarama .
I appreciate the help.