There are Volvo Bus (Vayu Vajra) shuttle service from city to Bangalore International Airport (BIAL). You can find the details at http://www.bmtcinfo.com/site/BSBusServicesDetails.jsp?bsserviceid=1. Click on the route link you think relevant to you, details of the route is mentioned. On the rightside there is button (not very intuitive) clicking you can view a google map with stops marked.
You can download a route list at http://www.bmtcinfo.com/uploads/Files/Vayu_Vajra_route_List.pdf.
At the airport bus terminal (which is just in front of the main entrance), there is route map displayed which is very useful, different routs ard marked in different colour.
Vayu Vajra buses are having ample space for keeping the luggage.
On the whole it is very good service, even though it is expensive (about Rs 150 to the city)