Well 50 minutes is not a relaxed transfer time at an airport set up for smooth and efficient connections, and FRA certainly isn’t one of those! On the plus side, you’re going Schengen to Schengen, so if you’re lucky both flights be on a bridge and in one part of A, meaning you’d have no passport check, no security, and a short walk. A bus arrival makes things a bit slower in your case- the bus points for disembarking pax at FRA T1 are still a weird and complex form of science. Even so, it should be possible to go straight up to the A gates from where the bus driver should let you out (if she/he knows the right place to open the door, which isn’t always the case.)

All in all I’d say you have a chance but not better than that…