Here' another quickish reply mate...
In the last couple of years there have been major upgrades to the bus services linking the major cities/coastal resorts in CY, but Kakopetria is off that map.
Taxi from LCA to the village ... gosh!... It's quite a way so It'll be pricey, be surprised if it were less than 100 euros.
To be honest, and have holidayed in CY many, many times... and know it's not the best environmental option but it's difficult to do CY without hiring a car. Car hire prices are pretty decent, a smallish saloon for around 25-30 Euros a day, even in peak season.
If you're still keen on buses have a look at
http://www.cyprusbybus.com/ .