If you are travelling on a friday, there should also be a 1225 departure to Stuttgart. So if you are missng the flight because of a delay, it will be 3 hours max.
You should not worry too much. If the flight arrives at 0925 sharp, it might be a problem (but still doable if you really hurry up and do some really fast walking once off the bus). But flight time usually is, IIRC, less than an hour, so there is a buffer built into the schedule. I would not count on arriving with your bags, though, if you check them in. KLM has lost my bags quite a few times at AMS on short connections (they all showed up a day or two later, though).