Rachael, I'm not familiar with Riu Bachata, but have the impression it is not on the Playa Dorada side of Puerto Plata. Correct? If so, you would need to get to the Central Park of Puerto Plata and start from there with public transportation. Ask at the hotel how you get to Puerto Plata. I am sure there is public transportation available. All those Dominican employees don't take taxis.
To get to Sosua and Cabarete from Puerto Plata via public transportation, you have two options: guaguas and publicos (public cars). Guaguas are mostly vans. They leave from the Central Park, make a stop on the outskirts of Puerto Plata to pick up more passengers, then leave for Sosua. After making that pick-up stop, they will probably be full, but will continue to pick up people along the road, squeezing them in. The cost from Puerto Plata to Sosua is RD$10/person. Try to have the correct amount for your party because being a tourist, you aren't likely to get change. The loading point at the park for the guaguas is the corner of Separacion and, I believe, Beller. Tell anyone in the park (except a cab driver) you want the guagua to Sosua and they will point you in the right direction. (I said mostly guaguas because they have started replacing the vans with buses. But they only have a few, so you can't be sure you would get on one of them unless you waited an indefinite period of time.)
The publicos pass by the park on Separacion and then turn at the corner of Beller. They are cars and have a red box on top that says PtoPta-Sosua. Their maximum load is 4 in the back seat and 2 in front with the driver. The price is RD$15/person. You have a couple of good options with these cars. One is to pay for the 6 seats, which is RD$90. Just give the driver RD$100 and indicate you are paying for all the seats. Taking a taxi from the park to Sosua would cost you RD$300. Or if there are only 2, for example, in your party, give the driver RD$60 and pay for the back seat. 4 in the back is crowded, 2 is quite comfortable. When you get to Sosua, they will drop you off on the highway across from the Texaco station. The street that passes along side is a short block and takes you to the main street. When you get ready to return, you can get one of these publicos back to Puerto Plata. Going that direction, they load on same side of the street as the Texaco. Again, buy the car, back seat, or if alone, pay RD$30 for the front seat so that you don't have anyone else but the driver.
If going to Cabarete, the guaguas continue on to Cabarete and further east. Or you can take a publico to Sosua, then switch to the car with the blue box on top that will be loading very close to where the car with the red box dropped you off. All of this is in the vicinity of the Texaco station. You can't miss it. The going rate to Cabarete from Sosua is RD$7/person. When you get to Cabarete, the first town you come to after leaving Sosua, you can get out on the main street. The road through Cabarete is the main street. When you are ready to return, flag down one of the cars with the blue box, take it to the Texaco station in Sosua, switch to the car with the red box on top.
This probably all sounds daunting to you, but it isn't. I really hope you will give it a try. You will save a lot of money, compared to taking taxis, and you will get a little better feeling for life in this country. Be adventuresome, Rachael.