Don't know is if you came across this site on your search but it's in English. Apparently the bus runs until 23.00hrs, there's a timetable that will download.

http://www.blualghero-sardinia.com/en/exploring/bus-transfers-alghero-airport-connections/

Your right about the cost of private transfers even a shared shuttle is expensive considering the distance.

Thank you Glynis,

I had found something similar but hadn't come across this site, it is in English but after consulting google maps none of the stops listed appear to be near our accommodation (not exactly sure how big Alghero is), on google maps there is a bus stop about 100yards from our destination and if you click on it it lists three different bus numbers, none of which match the on on the website.
I have read that you can purchase bus tickets from machines at the airport so we might have to chance (hope we can find someone English speaking) on arrival, we don't go until the end of October so plenty of time yet.

Your welcome Colin, I hope you manage to get sorted.

Please come back & let us know about your stay as never heard of the city before 👍