Limone is just within the province of Brescia who do an interesting English language site here
. Unfortunately some of the links don't work - most notably public transport. I've tracked the timetables down to here
but only in Italian. Pick Limone from the drop down list of towns and it will give a list of routes with PDF format timetables. There is also a more complicated site from Lombardy Region here
which also includes the boats, pick the option that starts Visualizza..
and then the first option and type Limone in the box.
The main bus service to Limone is from Desanzano railway station and takes about 90 minutes, it shows the Hotels L.da Vinci and Panorama as specific stops if that's any help. But note the last bus from Desanzano is at 18:30 and be aware that the note fer
means workdays (inc Saturday) and fest
There is a very limited service from Brescia bus station close to the railway station which would make the journey from the airport quicker if you were lucky enough to connect with the train. Unfortunately the direct Airport-Brescia coaches don't connect, otherwise this would have been the ideal option.