The fact is you can take an express gua gua - grande with a/c and wifi (usually) from Friusa to La Romana. You can get off that gua gua at the BAYAHIBE parada in La Romana. Just tell the cobrador that is where you want to get off. From that Bayahibe stop, you can take the smaller gua gua to Bayahibe. Express from Friusa to La Romana is 225 pesos. La Romana to Bayahibe is 60 pesos. The Bayahibe guas guas are not at parque central - they are at their own stop near Jumbo.
Friusa is a 40 dollar taxi ride from PUJ. You can try to catch that express bus by going from PU to Veron instead of Friusa - but it is little more challeging. A taxi driver should be able to get you there - and it costs $10 I think. But, of course for either, you need to know the hours. They start in the morning and then I know 10:50 am, 1:20 pm., and 3:50 pm from Friusa. So the bus arrives in Veron after leaving Friusa about 30 minutes later. Yes, you can go to Higuey but you don't want to. Smaller gua gua and more time.
Jeepito is right about the hard way, get off at Bayahibe highway exit. Very challenging to get off, walk to underpass and flag down small gua gua coming from La Romana. There are moto conchos there too, but not a safe ride to Bayahibe.
Taxi is the most safe and sure if you are not experienced here. And if you have anything bigger than a small suitcase, the small gua gua from La Romana to Bayahibe will not work well, or at all. No space inside the gua gua - its mostly used by people that live in La Romana and work in Bayahibe.