quick message today. I’m surprised, there is really a bus connection from Limassol to Nicosia and the other way around.
You’ll find more information here: http://www.nicosiabuses.com.cy/cityroutes.html
This bus service offer also connections to other places of interest. Have a look if you find your destination. But the webpage is really old… there are still Cyprus pounds shown
And for an airport connection you’ll find information here: http://www.cyprus-airport-transfer.co.uk