Yes, there is a bus service. But ALSA sometimes like to keep it quiet, so much so that it doesn't always appear on their timetables. Try clicking HERE and hopefully you might be able to check timetables for the specific dates that you are interested in.

David

We got an AlSA bus to Calpe from the Europa but had to buy our tickets in advance. (The day before I think ) but it was a couple of years ago.
On our return, we didn't realise that you had to get your ticket endorsed by the guy in the office at the bus depot in Calpe before you board the bus.
We just got on with our return tickets like you would at home but got a good telling off from the driver for not doing so although he did let us off in the end after we gave him a big smile and apologised profusely.
It was really nice for a day out and it was market day so we got a few bargains.

Sue

The train also goes to Calpe, but its a bit of a walk down to the sea or you can catch the bus down.

I've not been on it, but I think there is a boat that runs between the marina and Calpe. You probably don't get much time for sight seeing but if you just want a quick look around it might be OK.