The availability of buses in Cyprus is much better now than it was several years ago. Nevertheless, there is no direct bus from Larnaca to Paphos. There is an airport in Paphos so you can fly there instead of Larnaca.

There is a shuttle from Larnaca to Paphos but this does involve a bus change in Limassol with a connection that should not be more than 1 hour.

I don't know anyone who has used it so I cannot comment on the service.

Have you considered hiring a car? They are not expensive and if you have any plans to see more than Paphos, a car is recommended.