Time appreciation needs to consider
-Plane arrival often means the time the plane touches the runway.
-In my experience, planes almost never arrive on time.
-Taxi time to the unload gate is on your time.
-deplane takes 30 minutes.
-baggage can take another 30 minutes (and more).
-customs is no-nonsense (unlike the impertinent quiz at Canada customs) but the line can be long.
-You should allow minimum 1 hour to get to the point of being ready for onward travel.
-Time needed to get oriented and get to the shuttle stop. You can save a bit of time by looking at the airport map. 5 minutes.
-shuttle runs every ten minutes. Assume you just missed it and have to wait the full ten. Travel time is 15 minutes ... then you have to get from the shuttle stop to the bus stop. ~25 minutes.
-The bus leaves on schedule (unlike here in Canada); you and your bags have to be on it before, not at, departure time.
In my estimation, 1:15 is not enough time. (even with only carry-on-luggage)
Aena Madrid Airport Shuttle
http://www.aena.es/en/madrid-barajas-airport/transport-between-terminals.html