Bus to Riu - To catch bus from airport you have to get to the bus stop on the main road (dont worry, there is only one). You can either walk, which is about a mile, or you can take a cab there (negoitate the rate first). Buses going to the right (facing away from airport) goes towards Coco Beach/Sardinal area. Buses going left (across street) goes towards Liberia area. You want to get on the bus going Right. Just hop on the bus by the bus stop and pay the driver in 370Colones (I am not sure if they take USD). Tell the driver that you want to get off at Sardinal (its a park there that all the cabs hang out). From there you will need to catch a taxi for about $15-$20(again depends how well you negoitate). This method of transportation is not ideal for people with large suitcases or for more than 2people (cheaper and less hassle to take a cab direct from the airport).
There is no public bus that goes directly to Riu resort.
I read on other posts about a water taxi from Coco beach, I did not see any commercial service like this. All there was on the beach were the water sports guy with there small boats. The hotel does provide a round trip service to Coco beach during the day for $10 per person. Runs during the day only.